Question

1. 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?

2. There are 6 girls and 7 boys in a class. A team of 10 players is to be selected from the class. If the selection is random, what is the probability of selecting a team of 5 girls and 5 boys? what is the decimal?

Answer 1

Answer: 1. 286 different combinations of players are possible.

2. The probability of selecting a team of 5 girls and 5 boys is
`(63)/(143)` and the decimal is 0.4405...

Explanation:

1. Number of girls is 6 and number of boys is 7.

So, the total number of players = 6+7 = 13

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

So, the total possible number of different combinations of players will be:
`^1^3C_(10) = (13!)/(10! (13-10)!)=(13*12*11*10!)/(10!*3!)= (13*12*11)/(6)=286`

2. Number of girls is 6 and number of boys is 7.

The possible number of teams by selecting 5 girls and 5 boys will be:
`^6C_(5)* ^7C_(5) =6* 21= 126`

and the number of total possible teams of 10 players
`= ^1^3C_(10) =286`

Thus, the probability of selecting a team of 5 girls and 5 boys
`=(126)/(286)= (63)/(143)` or
`0.4405...`