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8 Choose 2 = 28

There are 28 ways to choose 2 items from 8 when order does not matter. It is the number of unordered pairs in a group of 8 — for example, handshakes between 8 people.

Combinations (8C2)
28
Permutations (8P2)
56

How 8 choose 2 is calculated

The combinations formula is C(n, r) = n! / (r! × (n − r)!). Substituting n = 8 and r = 2 gives:

C(8, 2) = 8! / (2! × 6!)
        = 56 / 2
        = 28

The 6! in the denominator cancels all but the top 2 factors of 8!, so 8 choose 2 is the product of 2 descending terms starting at 8, divided by 2!. That product, 56, is the number of ordered arrangements (8P2); dividing by 2! = 2 removes the duplicate orderings and leaves 28.

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