Question

A swim team consists of 6boys 7 girls a relay team 4 swimmers is chosen at random fr team members what is the probability that there are 3 boys in the relay team given that there is 1 girl on the relay team?

Answer 1

`(28)/(143)`

Explanation:

We need to choose 4 swimmers from 6boys and 7 girls.

Total swimmers, both boys and girls are (6 + 7) = 13.

From 13 swimmers 4 swimmers can be chosen in 13C4 =
`(13!)/(4! times 9!)` =
`55times13` ways.

It is also given that we should choose 3 boys for the relay team from total 6 boys. From total of 6 boys, 3 boys can be chosen in 6C3 =
`(6!)/(3!times3!)` = 20 ways.

From 7 girls, 1 girl can be chosen in 7C1 = 7 ways.

Hence, the required probability is
`(7times20)/(55times13)` =
`(7times4)/(11times13) = <strong>(28)/(143)`