A combination problem

There are 13 qualified applicants for 4 trainee positions in a fast food management program. How many different groups of trainees can be selected?

Here the order in which the trainees are chosen in not important. Therefore, you can just use the combination formula to solve this problem.

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

n = 13 and r = 4

C(13,4) = 13! / 4!(13-4)!

C(13,4) = 13! / 4!(9)!

C(13,4) = (13 × 12 × 11 × 10 × 9!) / 4!(9)!

C(13,4) = (13 × 12 × 11 × 10) / 4!

C(13,4) = (17160) / 24

C(13,4) = (17160) / 24

C(13,4) = 715

The number of different groups of trainees is 715

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