Question

State if each scenario involves a permutation or a combination. Then find the number of possibilities.

The batting order for seven players on a 8 person team.

a)Permutations: 120.960

b)Combinations: 20,160

c)Permutations: 40320

d)Combinations: 8

Answer 1

c) Permutations: 40320

Explanation:

We have that permutations are groupings in which the order of the objects matters. Combinations are groupings where content matters but order does not.

In this case, then the batting order, therefore the order does matter, therefore, it would be a permutation, where n = 8 and r = 7

nPr = n! / (n-r)!

Replacing:

8P7 = 8! / (8-7)! = 40320

Which means that the answer is c) Permutations: 40320