A display team wants to count possible arrangements of a small row of distinct products. Factorial turns that question into a compact recursive example, with a deliberately small input range so the demonstration stays understandable and safe.
Five distinct products can be arranged in 120 different orders. That result gives factorial a recognizable purpose: deciding how quickly the number of display possibilities grows. The sample reports the product count beside the arrangement count, so a reader does not have to guess what a lone number means or assume that the page actually generates every possible display arrangement.

Build the working example
const data = 5;
const result = (()=>{if(!Number.isInteger(data)||data<0||data>12)return 'Enter an integer from 0 to 12';function factorial(n){if(n===0)return 1;return n*factorial(n-1);}return {items:data,arrangements:factorial(data)};})();
console.log(result);
The function returns 1 when it reaches zero, its base case. Otherwise it multiplies the current value by the result for one fewer item. Five therefore produces 120 arrangements. The 0 to 12 validation happens before the first recursive call.
Factorial solves this problem by reducing it to a smaller version of the same problem. For five items, it multiplies 5 by the answer for four. That call multiplies 4 by the answer for three, continuing until factorial 0 returns 1. The calls then finish in reverse order, producing 120. The zero case is not a missing calculation: it is the base case that lets every earlier call finish. This differs from a loop because the function invokes itself and waits for a smaller result. The input validation happens before the first invocation and restricts the count to integers from 0 through 12.
The original input returns:
{
"items": 5,
"arrangements": 120
}

<!doctype html><html lang="en"><head><meta charset="utf-8"><meta name="nos-demo-layout" content="responsive-lab"><meta name="viewport" content="width=device-width,initial-scale=1"><title>Product arrangement counter</title><style>*{box-sizing:border-box}body{margin:0;background:#edf1f0;color:#172d36;font:15px/1.5 system-ui,sans-serif}main{max-width:1040px;margin:auto;padding:24px}header{display:flex;justify-content:space-between;gap:12px;align-items:center;margin-bottom:20px}.eyebrow{font-size:11px;font-weight:800;letter-spacing:2px;color:#55716b;text-transform:uppercase}h1{font-size:clamp(23px,4vw,34px);line-height:1.15;margin:8px 0}h2{font-size:16px;margin:0 0 12px}.tag{border:1px solid #bfceca;border-radius:99px;padding:6px 12px;font-size:12px;white-space:nowrap}.panel{background:white;border:1px solid #d4dfdb;border-radius:18px;padding:20px;margin-bottom:14px;box-shadow:0 9px 30px #1d393407}.grid{display:grid;grid-template-columns:1fr 1fr;gap:14px}.result{background:#17352f;color:#f7fffb}.result h2{color:#c9ded5}.cards{display:grid;gap:10px;grid-template-columns:repeat(auto-fit,minmax(135px,1fr))}.card{background:#f2ffc2;color:#17352f;padding:15px;border-radius:12px;min-width:0;overflow-wrap:anywhere}.card small{display:block;color:#536f60;font-size:11px;font-weight:700;text-transform:uppercase;margin-bottom:4px}.field{display:block;margin:8px 0}.field small{margin:0 0 3px;text-transform:none}.value{font-size:15px;font-weight:650;white-space:pre-wrap}.hero{font-size:clamp(28px,5vw,46px);font-weight:750;line-height:1.2;overflow-wrap:anywhere}.muted{color:#587169;font-size:13px}.result .muted{color:#bed7cb}pre{margin:0;white-space:pre-wrap;overflow-wrap:anywhere;font:13px/1.6 ui-monospace,monospace;max-height:220px;overflow:auto}.toolbar{display:flex;flex-wrap:wrap;gap:8px;margin:12px 0}button{background:#17352f;color:white;border:0;border-radius:10px;padding:10px 14px;font:600 13px system-ui;cursor:pointer}button.secondary{background:#edf3ea;color:#244337;border:1px solid #d0ddd0}button:hover{filter:brightness(.94)}button:focus-visible,textarea:focus-visible,summary:focus-visible{outline:3px solid #749919;outline-offset:3px}textarea{display:block;width:100%;height:126px;border:1px solid #bccfc5;border-radius:10px;background:#fafcf9;padding:12px;font:13px/1.5 ui-monospace,monospace;resize:vertical;color:#15362c}label{font-weight:650;font-size:13px}details{margin-top:16px}summary{cursor:pointer;font-size:13px;font-weight:650}#status{min-height:20px;font-size:12px;color:#526f60;margin-top:8px}.error{color:#ffcfbf}.footer{font-size:12px;color:#627b72;margin-top:16px}.empty{font-size:18px;color:#c7dacd}.source-card{background:#f4f7f3;border:1px solid #dbe4d8;border-radius:10px;padding:12px;overflow-wrap:anywhere;white-space:pre-wrap}.source-list{display:flex;flex-wrap:wrap;gap:8px;max-height:170px;overflow:auto}.source-list .source-card{flex:1;min-width:100px}.code{background:#f5f8f2}mark{background:#f2ffc2;color:#183a2d;padding:2px 5px;border-radius:4px}@media(max-width:620px){main{padding:15px}.grid{grid-template-columns:1fr}.panel{padding:16px}header{align-items:flex-start}.tag{display:none}h1{font-size:25px}.cards{grid-template-columns:repeat(auto-fit,minmax(125px,1fr))}.source-list{max-height:120px}pre{max-height:150px}}</style></head><body><main>
<header><div><div class="eyebrow">JavaScript • Language recursion</div><h1>Product arrangement counter</h1><div class="muted">One input, one operation, one observable result.</div></div><span class="tag">Starter example</span></header>
<section class="panel"><label for="input">Input data (JSON)</label><textarea id="input" maxlength="10000" spellcheck="false"></textarea><div class="toolbar"><button id="run" type="button">Update preview</button><button class="secondary" id="original" type="button">Original data</button><button class="secondary" id="changed" type="button">Changed data</button><button class="secondary" id="edge" type="button">Empty / zero case</button></div><div id="status" role="status" aria-live="polite"></div></section>
<div class="grid"><section class="panel code"><h2>The operation</h2><pre id="expression"></pre></section><section class="panel result"><h2>Returned result</h2><pre id="result" aria-live="polite"></pre></section></div><section class="panel"><h2>Source after the operation</h2><pre id="source"></pre></section>
<p class="footer">Local sample data only. No server request, account, or installation is needed.</p></main><script>
'use strict';
const initial = "5";
const alternate = "6";
const empty = "0";
const input = document.getElementById('input');
const output = document.getElementById('result');
const source = document.getElementById('source');
const status = document.getElementById('status');
function transform(data) { return (()=>{if(!Number.isInteger(data)||data<0||data>12)return 'Enter an integer from 0 to 12';function factorial(n){if(n===0)return 1;return n*factorial(n-1);}return {items:data,arrangements:factorial(data)};})(); }
function readable(value) {
if (value === undefined) return 'undefined';
if (typeof value === 'number' && Object.is(value, -0)) return '-0';
return JSON.stringify(value, (_, v) => typeof v === 'number' && !Number.isFinite(v) ? String(v) : v, 2);
}
function renderCards(value, host) {
host.replaceChildren();
if (Array.isArray(value)) {
if (!value.length) {const p=document.createElement('p');p.className='empty';p.textContent='No items returned';host.append(p);return;}
const grid=document.createElement('div');grid.className='cards';
value.slice(0,40).forEach((item,index)=>{const card=document.createElement('div');card.className='card';const label=document.createElement('small');label.textContent='Item '+(index+1);card.append(label);appendValue(item,card);grid.append(card);});host.append(grid);
if(value.length>40){const p=document.createElement('p');p.textContent='Showing 40 of '+value.length+' items.';host.append(p);}
} else if(value && typeof value==='object'){const card=document.createElement('div');card.className='card';appendValue(value,card);host.append(card);}
else {const p=document.createElement('div');p.className='hero';p.textContent=typeof value==='boolean'?(value?'Yes · true':'No · false'):value===undefined?'No value · undefined':value===''?'Empty string':String(value);host.append(p);}
}
function appendValue(value,host){
if(value && typeof value==='object' && !Array.isArray(value))Object.entries(value).slice(0,40).forEach(([key,item])=>{const row=document.createElement('div');row.className='field';const label=document.createElement('small');label.textContent=key;const text=document.createElement('span');text.className='value';text.textContent=typeof item==='string'?item:readable(item);row.append(label,text);host.append(row);});
else {const text=document.createElement('div');text.className='value';text.textContent=typeof value==='string'?value:readable(value);host.append(text);}
}
function update(){
try{
if(input.value.length>10000)throw new Error('Keep this sample below 10,000 characters.');
const data=JSON.parse(input.value);const before=readable(data);const result=transform(data);const after=readable(data);
output.textContent=readable(result);source.textContent=after;
output.classList.remove('error');status.textContent='Preview updated. '+(before===after?'Data values unchanged.':'Source data changed in place.');
}catch(error){output.replaceChildren();output.classList.add('error');output.textContent=error.name+': '+error.message;source.replaceChildren();status.textContent='Check the JSON and the input shape. Restore Original data to start again.';}
}
document.getElementById('run').addEventListener('click',update);
[['original',initial],['changed',alternate],['edge',empty]].forEach(([id,value])=>document.getElementById(id).addEventListener('click',()=>{input.value=value;update();}));
document.getElementById('expression').textContent="(()=>{if(!Number.isInteger(data)||data<0||data>12)return 'Enter an integer from 0 to 12';function factorial(n){if(n===0)return 1;return n*factorial(n-1);}return {items:data,arrangements:factorial(data)};})()";
input.value=initial;update();
</script></body></html>
Test the boundary that matters
Change the input to 3 and expect arrangements 6. Change it to 0 and expect arrangements 1, the base case result. A decimal, a negative value, or 13 should return the validation message instead of beginning recursive work. The upper limit avoids excessive calls and keeps this small factorial calculation comfortably within exact integer results. It is also important to distinguish counting arrangements from constructing them: this function creates one result object, not a list containing every possible product order, which would become large much sooner.

<!doctype html><html lang="en"><head><meta charset="utf-8"><meta name="nos-demo-layout" content="responsive-lab"><meta name="viewport" content="width=device-width,initial-scale=1"><title>Product arrangement counter</title><style>*{box-sizing:border-box}body{margin:0;background:#edf1f0;color:#172d36;font:15px/1.5 system-ui,sans-serif}main{max-width:1040px;margin:auto;padding:24px}header{display:flex;justify-content:space-between;gap:12px;align-items:center;margin-bottom:20px}.eyebrow{font-size:11px;font-weight:800;letter-spacing:2px;color:#55716b;text-transform:uppercase}h1{font-size:clamp(23px,4vw,34px);line-height:1.15;margin:8px 0}h2{font-size:16px;margin:0 0 12px}.tag{border:1px solid #bfceca;border-radius:99px;padding:6px 12px;font-size:12px;white-space:nowrap}.panel{background:white;border:1px solid #d4dfdb;border-radius:18px;padding:20px;margin-bottom:14px;box-shadow:0 9px 30px #1d393407}.grid{display:grid;grid-template-columns:1fr 1fr;gap:14px}.result{background:#17352f;color:#f7fffb}.result h2{color:#c9ded5}.cards{display:grid;gap:10px;grid-template-columns:repeat(auto-fit,minmax(135px,1fr))}.card{background:#f2ffc2;color:#17352f;padding:15px;border-radius:12px;min-width:0;overflow-wrap:anywhere}.card small{display:block;color:#536f60;font-size:11px;font-weight:700;text-transform:uppercase;margin-bottom:4px}.field{display:block;margin:8px 0}.field small{margin:0 0 3px;text-transform:none}.value{font-size:15px;font-weight:650;white-space:pre-wrap}.hero{font-size:clamp(28px,5vw,46px);font-weight:750;line-height:1.2;overflow-wrap:anywhere}.muted{color:#587169;font-size:13px}.result .muted{color:#bed7cb}pre{margin:0;white-space:pre-wrap;overflow-wrap:anywhere;font:13px/1.6 ui-monospace,monospace;max-height:220px;overflow:auto}.toolbar{display:flex;flex-wrap:wrap;gap:8px;margin:12px 0}button{background:#17352f;color:white;border:0;border-radius:10px;padding:10px 14px;font:600 13px system-ui;cursor:pointer}button.secondary{background:#edf3ea;color:#244337;border:1px solid #d0ddd0}button:hover{filter:brightness(.94)}button:focus-visible,textarea:focus-visible,summary:focus-visible{outline:3px solid #749919;outline-offset:3px}textarea{display:block;width:100%;height:126px;border:1px solid #bccfc5;border-radius:10px;background:#fafcf9;padding:12px;font:13px/1.5 ui-monospace,monospace;resize:vertical;color:#15362c}label{font-weight:650;font-size:13px}details{margin-top:16px}summary{cursor:pointer;font-size:13px;font-weight:650}#status{min-height:20px;font-size:12px;color:#526f60;margin-top:8px}.error{color:#ffcfbf}.footer{font-size:12px;color:#627b72;margin-top:16px}.empty{font-size:18px;color:#c7dacd}.source-card{background:#f4f7f3;border:1px solid #dbe4d8;border-radius:10px;padding:12px;overflow-wrap:anywhere;white-space:pre-wrap}.source-list{display:flex;flex-wrap:wrap;gap:8px;max-height:170px;overflow:auto}.source-list .source-card{flex:1;min-width:100px}.code{background:#f5f8f2}mark{background:#f2ffc2;color:#183a2d;padding:2px 5px;border-radius:4px}@media(max-width:620px){main{padding:15px}.grid{grid-template-columns:1fr}.panel{padding:16px}header{align-items:flex-start}.tag{display:none}h1{font-size:25px}.cards{grid-template-columns:repeat(auto-fit,minmax(125px,1fr))}.source-list{max-height:120px}pre{max-height:150px}}</style></head><body><main>
<header><div><div class="eyebrow">JavaScript • Language recursion</div><h1>Product arrangement counter</h1><div class="muted">Change the data. See the actual result.</div></div><span class="tag">Interactive prototype</span></header>
<section class="panel"><label for="input">Input data (JSON)</label><textarea id="input" maxlength="10000" spellcheck="false"></textarea><div class="toolbar"><button id="run" type="button">Update preview</button><button class="secondary" id="original" type="button">Original data</button><button class="secondary" id="changed" type="button">Changed data</button><button class="secondary" id="edge" type="button">Empty / zero case</button></div><div id="status" role="status" aria-live="polite"></div></section>
<div class="grid"><section class="panel"><h2>Source after the operation</h2><div id="source" class="source-list"></div><p id="source-status" class="muted"></p></section><section class="panel result"><h2>Returned result</h2><div id="result" aria-live="polite"></div></section></div><details class="panel code"><summary>Inspect the exact values</summary><pre id="inspect"></pre></details>
<p class="footer">Local sample data only. No server request, account, or installation is needed.</p></main><script>
'use strict';
const initial = "5";
const alternate = "6";
const empty = "0";
const input = document.getElementById('input');
const output = document.getElementById('result');
const source = document.getElementById('source');
const status = document.getElementById('status');
function transform(data) { return (()=>{if(!Number.isInteger(data)||data<0||data>12)return 'Enter an integer from 0 to 12';function factorial(n){if(n===0)return 1;return n*factorial(n-1);}return {items:data,arrangements:factorial(data)};})(); }
function readable(value) {
if (value === undefined) return 'undefined';
if (typeof value === 'number' && Object.is(value, -0)) return '-0';
return JSON.stringify(value, (_, v) => typeof v === 'number' && !Number.isFinite(v) ? String(v) : v, 2);
}
function renderCards(value, host) {
host.replaceChildren();
if (Array.isArray(value)) {
if (!value.length) {const p=document.createElement('p');p.className='empty';p.textContent='No items returned';host.append(p);return;}
const grid=document.createElement('div');grid.className='cards';
value.slice(0,40).forEach((item,index)=>{const card=document.createElement('div');card.className='card';const label=document.createElement('small');label.textContent='Item '+(index+1);card.append(label);appendValue(item,card);grid.append(card);});host.append(grid);
if(value.length>40){const p=document.createElement('p');p.textContent='Showing 40 of '+value.length+' items.';host.append(p);}
} else if(value && typeof value==='object'){const card=document.createElement('div');card.className='card';appendValue(value,card);host.append(card);}
else {const p=document.createElement('div');p.className='hero';p.textContent=typeof value==='boolean'?(value?'Yes · true':'No · false'):value===undefined?'No value · undefined':value===''?'Empty string':String(value);host.append(p);}
}
function appendValue(value,host){
if(value && typeof value==='object' && !Array.isArray(value))Object.entries(value).slice(0,40).forEach(([key,item])=>{const row=document.createElement('div');row.className='field';const label=document.createElement('small');label.textContent=key;const text=document.createElement('span');text.className='value';text.textContent=typeof item==='string'?item:readable(item);row.append(label,text);host.append(row);});
else {const text=document.createElement('div');text.className='value';text.textContent=typeof value==='string'?value:readable(value);host.append(text);}
}
function update(){
try{
if(input.value.length>10000)throw new Error('Keep this sample below 10,000 characters.');
const data=JSON.parse(input.value);const before=readable(data);const result=transform(data);const after=readable(data);
renderCards(result,output);source.replaceChildren();(Array.isArray(data)?data.slice(0,40):[data]).forEach(item=>{const card=document.createElement('div');card.className='source-card';card.textContent=typeof item==='string'?item:readable(item);source.append(card);});document.getElementById('source-status').textContent=before===after?'Data values unchanged':'Data values changed in place';document.getElementById('inspect').textContent='Input before:\n'+before+'\n\nReturned result:\n'+readable(result)+'\n\nSource after:\n'+after;
output.classList.remove('error');status.textContent='Preview updated. '+(before===after?'Data values unchanged.':'Source data changed in place.');
}catch(error){output.replaceChildren();output.classList.add('error');output.textContent=error.name+': '+error.message;source.replaceChildren();document.getElementById('source-status').textContent='';document.getElementById('inspect').textContent='';status.textContent='Check the JSON and the input shape. Restore Original data to start again.';}
}
document.getElementById('run').addEventListener('click',update);
[['original',initial],['changed',alternate],['edge',empty]].forEach(([id,value])=>document.getElementById(id).addEventListener('click',()=>{input.value=value;update();}));
input.value=initial;update();
</script></body></html>
Recursion needs a reachable base case and progress toward it. Factorial grows quickly, and larger JavaScript integers lose exactness; this example intentionally rejects counts above 12.
If the complete page stops before producing a result, compare it with the checks in HTML JavaScript not working.
Make one useful change
Compare counts 0,3, and 5, then remove the decrement only on paper. Explain why the unchanged argument would never reach the base case.
For the exercise, the expected arrangement counts are 1 for zero,6 for three, and 120 for five. Trace the five item case until you can point to the call that stops the recursion. Removing the decrement would keep passing the same positive value forever until the runtime fails. Removing the base case would also prevent a successful return. Keep both the decreasing argument and the stopping case whenever you adapt recursive code to a different task.
A display planner can now inspect how quickly even a small product lineup becomes difficult to compare manually. Share the complete arrangement counter with NOS and ask them to try three and five items. The page communicates the size of the choice clearly, while any actual shortlist or visual arrangement generator can remain a separate planning feature.
For the exact syntax and behavior, see MDN: recursion.