Combination and Permutation Calculator
:root {
–primary-blue: #004a99;
–success-green: #28a745;
–light-background: #f8f9fa;
–white: #ffffff;
–gray-border: #dee2e6;
–dark-text: #343a40;
}
body {
font-family: 'Segoe UI', Tahoma, Geneva, Verdana, sans-serif;
background-color: var(–light-background);
color: var(–dark-text);
line-height: 1.6;
margin: 0;
padding: 20px;
}
.loan-calc-container {
max-width: 800px;
margin: 30px auto;
background-color: var(–white);
padding: 30px;
border-radius: 8px;
box-shadow: 0 4px 15px rgba(0, 0, 0, 0.1);
border: 1px solid var(–gray-border);
}
h1, h2 {
color: var(–primary-blue);
text-align: center;
margin-bottom: 25px;
}
.input-section, .output-section {
margin-bottom: 30px;
padding: 20px;
border: 1px solid var(–gray-border);
border-radius: 5px;
background-color: var(–white);
}
.input-group {
margin-bottom: 15px;
display: flex;
flex-direction: column;
align-items: flex-start;
}
.input-group label {
font-weight: 600;
margin-bottom: 8px;
color: var(–primary-blue);
}
.input-group input[type="number"] {
width: calc(100% – 20px);
padding: 10px;
border: 1px solid var(–gray-border);
border-radius: 4px;
box-sizing: border-box; /* Include padding and border in the element's total width and height */
font-size: 1rem;
}
.input-group input[type="number"]:focus {
outline: none;
border-color: var(–primary-blue);
box-shadow: 0 0 0 2px rgba(0, 74, 153, 0.25);
}
button {
display: block;
width: 100%;
padding: 12px 20px;
background-color: var(–primary-blue);
color: var(–white);
border: none;
border-radius: 5px;
font-size: 1.1rem;
cursor: pointer;
transition: background-color 0.3s ease;
margin-top: 10px;
}
button:hover {
background-color: #003b7f;
}
.result-display {
background-color: var(–success-green);
color: var(–white);
padding: 20px;
text-align: center;
border-radius: 5px;
font-size: 1.5rem;
font-weight: bold;
margin-top: 20px;
box-shadow: 0 2px 10px rgba(40, 167, 69, 0.3);
}
.result-display span {
font-size: 1.2rem;
display: block;
margin-top: 5px;
}
.article-content {
margin-top: 40px;
padding: 30px;
background-color: var(–white);
border: 1px solid var(–gray-border);
border-radius: 5px;
}
.article-content h2 {
text-align: left;
color: var(–primary-blue);
margin-bottom: 15px;
}
.article-content p, .article-content ul, .article-content li {
margin-bottom: 15px;
}
.article-content code {
background-color: var(–light-background);
padding: 2px 5px;
border-radius: 3px;
font-family: Consolas, Monaco, 'Andale Mono', 'Ubuntu Mono', monospace;
}
/* Responsive adjustments */
@media (max-width: 768px) {
.loan-calc-container {
padding: 20px;
}
h1 {
font-size: 1.8rem;
}
button {
font-size: 1rem;
}
.result-display {
font-size: 1.3rem;
}
}
Combination and Permutation Calculator
Understanding Combinations and Permutations
In probability and statistics, combinations and permutations are fundamental concepts used to count the number of ways an event can occur. While both involve selecting items from a set, they differ in whether the order of selection matters.
Permutations
A permutation is an arrangement of objects in a specific order. When calculating permutations, the sequence in which items are chosen is significant. The formula for permutations of selecting 'k' items from a set of 'n' distinct items is:
P(n, k) = n! / (n - k)!
where '!' denotes the factorial (e.g., 5! = 5 * 4 * 3 * 2 * 1).
When to Use Permutations:
- Determining the number of ways to award 1st, 2nd, and 3rd place in a race.
- Arranging books on a shelf.
- Forming different words or codes from a set of letters.
Combinations
A combination is a selection of objects where the order of selection does not matter. In combinations, we are only concerned with the group of items chosen, not the sequence in which they were selected. The formula for combinations of selecting 'k' items from a set of 'n' distinct items is:
C(n, k) = n! / (k! * (n - k)!)
Notice that this is equivalent to the permutation formula divided by k!, acknowledging that all the different orderings of the same k items are counted as a single combination.
When to Use Combinations:
- Choosing a committee of 3 people from a group of 10.
- Selecting toppings for a pizza.
- Drawing cards from a deck where the order doesn't matter.
Example Calculation
Let's say you have 5 distinct items (n=5) and you want to choose 2 of them (k=2).
- Permutations: P(5, 2) = 5! / (5 – 2)! = 5! / 3! = (5 * 4 * 3 * 2 * 1) / (3 * 2 * 1) = 120 / 6 = 20. There are 20 different ordered arrangements.
- Combinations: C(5, 2) = 5! / (2! * (5 – 2)!) = 5! / (2! * 3!) = (5 * 4 * 3 * 2 * 1) / ((2 * 1) * (3 * 2 * 1)) = 120 / (2 * 6) = 120 / 12 = 10. There are 10 different unique groups.
This calculator helps you quickly determine these values for any given set of 'n' and 'k'.
// Helper function to calculate factorial
var factorial = function(num) {
if (num 1; i–) {
result *= i;
}
return result;
}
}
var calculateCombinationsAndPermutations = function() {
var n = parseInt(document.getElementById("nValue").value);
var k = parseInt(document.getElementById("kValue").value);
var resultsContainer = document.getElementById("resultsContainer");
var combinationResultDiv = document.getElementById("combinationResult");
var permutationResultDiv = document.getElementById("permutationResult");
// Clear previous results
combinationResultDiv.innerHTML = ";
permutationResultDiv.innerHTML = ";
resultsContainer.style.display = 'none';
// Input validation
if (isNaN(n) || isNaN(k)) {
combinationResultDiv.innerHTML = '
Please enter valid numbers for n and k.';
resultsContainer.style.display = 'block';
return;
}
if (n < 0 || k < 0) {
combinationResultDiv.innerHTML = '
n and k cannot be negative.';
resultsContainer.style.display = 'block';
return;
}
if (k > n) {
combinationResultDiv.innerHTML = '
k cannot be greater than n.';
resultsContainer.style.display = 'block';
return;
}
// Calculate factorial values
var nFactorial = factorial(n);
var kFactorial = factorial(k);
var nMinusKFactorial = factorial(n – k);
// Calculate Permutation P(n, k)
var permutation = nFactorial / nMinusKFactorial;
// Calculate Combination C(n, k)
var combination = nFactorial / (kFactorial * nMinusKFactorial);
// Display results
permutationResultDiv.innerHTML = 'Permutations P(n, k):
' + permutation.toLocaleString() + '' +
'
' + n + '! / (' + n + ' – ' + k + ')! = ' + n + '! / ' + (n – k) + '!';
combinationResultDiv.innerHTML = 'Combinations C(n, k):
' + combination.toLocaleString() + '' +
'
' + n + '! / (' + k + '! * (' + n + ' – ' + k + ')!) = ' + n + '! / (' + k + '! * ' + (n – k) + '!)';
resultsContainer.style.display = 'block';
}