A swim team must be chosen from 10 candidates. What is the greatest number of different four-person teams that can be chosen?

210 combinations

Step-by-step explanation:

The total number of candidates given = n = 10

The number of candidates to be chosen = r = 4

As in this, the sequence of the chosen candidates doesn't matter, we can use Combination to find the solution.

C(n,r) = n! / (n-r)! (r)!

where n = 10 and r = 4

C(10,4) = 10! / (10-4)! (4)!

C(10,4) = 10! / 6! 4!

C(10,4) = (10·9·8·7·6·5·4·3·2·1) / (6·5·4·3·2·1)(4·3·2·1)

C(10,4) = (10·9·8·7) / ((4·3·2·1))

C(10,4) = 210 combinations

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