🔢 Math Calculator

📐 How It Works

Counts unordered selections of r items from n — where choosing ABC is the same as BAC. Used in probability and statistics.

🔢 Worked Examples

• C(5,2) = 10
• C(10,3) = 120
• C(52,5) = 2,598,960 (poker hands)
• C(8,4) = 70
• C(n,0) = C(n,n) = 1

📋 Common Use Cases

• Lottery odds — C(49,6) = 13,983,816 for 6-of-49
• Poker hand probabilities
• Number of possible teams from a squad
• Statistics — binomial distribution coefficients

💡 Did You Know?

Pascal's Triangle lists all combinations: row n gives C(n,0), C(n,1), …, C(n,n). The row sums are 1, 2, 4, 8, …, 2ⁿ — the total number of subsets of n items.

⚠️ Common Mistake

Using combinations when order matters — a PIN or ranking requires permutations. The key test: does swapping two choices produce a different result? If yes, it's a permutation.