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52 Choose 2 = 1,326

There are 1,326 ways to choose 2 items from 52 when order does not matter. It is the number of two-card starting hands in a 52-card deck, where the two suits matter but the order does not.

Combinations (52C2)
1,326
Permutations (52P2)
2,652

How 52 choose 2 is calculated

The combinations formula is C(n, r) = n! / (r! × (n − r)!). Substituting n = 52 and r = 2 gives:

C(52, 2) = 52! / (2! × 50!)
         = 2,652 / 2
         = 1,326

The 50! in the denominator cancels all but the top 2 factors of 52!, so 52 choose 2 is the product of 2 descending terms starting at 52, divided by 2!. That product, 2,652, is the number of ordered arrangements (52P2); dividing by 2! = 2 removes the duplicate orderings and leaves 1,326.

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