52 Choose 14 = 1,768,966,344,600
There are 1,768,966,344,600 ways to choose 14 items from 52 when order does not matter. Order is ignored, so a 14-card holding is counted once however it was dealt.
Combinations (52C14)
1,768,966,344,600
How 52 choose 14 is calculated
The combinations formula is C(n, r) = n! / (r! × (n − r)!). Substituting n = 52 and r = 14 gives:
C(52, 14) = 52! / (14! × 38!)
= 1,768,966,344,600The 38! in the denominator cancels all but the top 14 factors of 52!, so 52 choose 14 is the product of 14 descending terms starting at 52, divided by 14!. Dividing by 14! = 87,178,291,200 removes the duplicate orderings, because each selection of 14 items can be arranged in 14! different ways.
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