6 Choose 3 = 20
There are 20 ways to choose 3 items from 6 when order does not matter. Each group of 3 is counted once, no matter which order its three members were picked in.
Combinations (6C3)
20
Permutations (6P3)
120
How 6 choose 3 is calculated
The combinations formula is C(n, r) = n! / (r! × (n − r)!). Substituting n = 6 and r = 3 gives:
C(6, 3) = 6! / (3! × 3!)
= 120 / 6
= 20The 3! in the denominator cancels all but the top 3 factors of 6!, so 6 choose 3 is the product of 3 descending terms starting at 6, divided by 3!. That product, 120, is the number of ordered arrangements (6P3); dividing by 3! = 6 removes the duplicate orderings and leaves 20.
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