12 Choose 4 = 495
There are 495 ways to choose 4 items from 12 when order does not matter. It answers questions like how many 4-person teams can be picked from 12 candidates.
Combinations (12C4)
495
Permutations (12P4)
11,880
How 12 choose 4 is calculated
The combinations formula is C(n, r) = n! / (r! × (n − r)!). Substituting n = 12 and r = 4 gives:
C(12, 4) = 12! / (4! × 8!)
= 11,880 / 24
= 495The 8! in the denominator cancels all but the top 4 factors of 12!, so 12 choose 4 is the product of 4 descending terms starting at 12, divided by 4!. That product, 11,880, is the number of ordered arrangements (12P4); dividing by 4! = 24 removes the duplicate orderings and leaves 495.
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