🔢 Math Calculator

📐 How It Works

Computes n! — the product of all positive integers from 1 to n. Factorials grow extremely fast and appear throughout combinatorics and probability.

🔢 Worked Examples

• 5! = 120
• 10! = 3,628,800
• 0! = 1 (by definition)
• 20! ≈ 2.43 × 10¹⁸
• 52! ≈ 8.07 × 10⁶⁷ (deck shuffles)

📋 Common Use Cases

• Number of ways to arrange n objects (permutations)
• Probability of specific card hands in poker
• Computing binomial coefficients C(n,k) = n!/(k!(n-k)!)
• Taylor series — sin(x) = x - x³/3! + x⁵/5! - …

💡 Did You Know?

There are 52! ≈ 8×10⁶⁷ ways to shuffle a standard deck of cards — more than the number of atoms in the observable universe. Every properly shuffled deck is almost certainly in an arrangement never seen before in history.

⚠️ Common Mistake

0! = 1, not 0. This is defined to make the formula C(n,0) = 1 consistent — there is exactly one way to choose nothing.