Question

There are 7 people on the cycling team: Laura, Deidra, Noelle, Ramona, Karen, Peg, and Uli. Their coach must pick two of them to be co-captains. How many different pairs can the coach choose?

Answer 1

The coach can choose 21 different pairs.

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
`nC_(r)`.

Therefore, number of ways of selecting 2 people from 7 people =
`7C_(2)`

`= (7!)/((7-2)!2!)`

`= ((7)(6)(5!))/(5!(2))`

= 7 × 3

= 21