5 Choose 2 = 10
There are 10 ways to choose 2 items from 5 when order does not matter. It is the textbook case of picking 2 options out of 5, such as two electives from a short list.
Combinations (5C2)
10
Permutations (5P2)
20
How 5 choose 2 is calculated
The combinations formula is C(n, r) = n! / (r! × (n − r)!). Substituting n = 5 and r = 2 gives:
C(5, 2) = 5! / (2! × 3!)
= 20 / 2
= 10The 3! in the denominator cancels all but the top 2 factors of 5!, so 5 choose 2 is the product of 2 descending terms starting at 5, divided by 2!. That product, 20, is the number of ordered arrangements (5P2); dividing by 2! = 2 removes the duplicate orderings and leaves 10.
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