Question

There are 6 girls and 7 boys in a class. A team of 10 players is to be selected from the class. How many different combinations of players are possible?]

Answer 1

This is a simple combination problem. Just take the number of girls and boys, which is 13 and take 10 of it at a time. 13C10 is 286.

Answer 2

In 286 different ways 10 players can be selected.

Explanation:

There are 6 girls and 7 boys in a class. So in total there are 6+7 = 13 number of students in the class.

A team of 10 players is to be selected from the class.

As there is no other conditions are given, we can pick any 10 students from 13 students.

The way we can select 10 players from 13 students is,

`=\dbinom{13}{10}`

`=(13!)/(10!(13-10)!)`

`=(13!)/(10!\ 3!)`

`=(13* 12* 11* 10!)/(10!\ 3!)`

`=(13* 12* 11)/(6)`

`=286`