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20 Choose 3 = 1,140

There are 1,140 ways to choose 3 items from 20 when order does not matter. It is a common probability-homework setup: 3 picks from a pool of 20.

Combinations (20C3)
1,140
Permutations (20P3)
6,840

How 20 choose 3 is calculated

The combinations formula is C(n, r) = n! / (r! × (n − r)!). Substituting n = 20 and r = 3 gives:

C(20, 3) = 20! / (3! × 17!)
         = 6,840 / 6
         = 1,140

The 17! in the denominator cancels all but the top 3 factors of 20!, so 20 choose 3 is the product of 3 descending terms starting at 20, divided by 3!. That product, 6,840, is the number of ordered arrangements (20P3); dividing by 3! = 6 removes the duplicate orderings and leaves 1,140.

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