Answer:
The coach can choose 21 different pairs.
Step-by-step explanation:
Picking 2 people out of 7 people is a selection and we should use combination formula.
The number of ways of selecting r things out of n things is [tex]nC_{r}[/tex].
Therefore, number of ways of selecting 2 people from 7 people = [tex]7C_{2}[/tex]
[tex]= \frac{7!}{(7-2)!2!}[/tex]
[tex]= \frac{(7)(6)(5!)}{5!(2)}[/tex]
= 7 × 3
= 21
