Question

Eight boys and seven girls showed up to one of the team's games. League rules limit each team to 10 players at a time (five girls and five boys) per game. Given this rule, how many combinations of 10 players are there among the 15 boys and girls who showed up at this particular game?

Answer 1

1176 Combinations

Explanation:

As mentioned in the question, there are total 8 boys and 7 girls.

Our objective is to create a team with 5 boys and girls each.

To select 5 boys out of 8, we will use combination.

=> 8C5 =
`(8!)/(5!(8-5!))`

=>
`(8.7.6.5!)/(5!.3!)`

=>
`(8.7.6)/(6)`

=> 56

Similarly,

5 girls are selected using 7C5

=> 21

Therefore, the total combination of players are 56 * 21 = 1176