52 Choose 13 = 635,013,559,600
There are 635,013,559,600 ways to choose 13 items from 52 when order does not matter. It is the number of possible 13-card bridge hands, which is why no two bridge deals ever repeat.
Combinations (52C13)
635,013,559,600
How 52 choose 13 is calculated
The combinations formula is C(n, r) = n! / (r! × (n − r)!). Substituting n = 52 and r = 13 gives:
C(52, 13) = 52! / (13! × 39!)
= 635,013,559,600The 39! in the denominator cancels all but the top 13 factors of 52!, so 52 choose 13 is the product of 13 descending terms starting at 52, divided by 13!. Dividing by 13! = 6,227,020,800 removes the duplicate orderings, because each selection of 13 items can be arranged in 13! different ways.
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