Answer:
35 four-person relay teams can be selected from the seven athletes.
Step-by-step explanation:
There are total 7 team mates in the Olympic team and we are required to select 4 member teams.
This is a combination problem since the order doesn't matter in this case.
[tex](n, k) = \frac{n!}{k!(n-k)!}[/tex]
Here we have n = 7 persons
We want to select 4 person team so k = 4
[tex]C(7, 4) = \frac{7!}{4!(7-4)!}[/tex]
[tex]C(7, 4) = \frac{7!}{4!(3)!}[/tex]
[tex]C(7, 4) = 35[/tex]
Therefore, 35 four-person relay teams can be selected from the seven athletes.
