calc.ing

52 Choose 5 = 2,598,960

There are 2,598,960 ways to choose 5 items from 52 when order does not matter. It is the number of distinct 5-card poker hands that can be dealt from a standard 52-card deck.

Combinations (52C5)
2,598,960
Permutations (52P5)
311,875,200

How 52 choose 5 is calculated

The combinations formula is C(n, r) = n! / (r! × (n − r)!). Substituting n = 52 and r = 5 gives:

C(52, 5) = 52! / (5! × 47!)
         = 311,875,200 / 120
         = 2,598,960

The 47! in the denominator cancels all but the top 5 factors of 52!, so 52 choose 5 is the product of 5 descending terms starting at 52, divided by 5!. That product, 311,875,200, is the number of ordered arrangements (52P5); dividing by 5! = 120 removes the duplicate orderings and leaves 2,598,960.

Calculate other values

Need a different n and r? The full calculator handles any values, including permutations, and gives you a shareable link for the result.

Open the n choose r calculator