Question

There are 6 girls and 7 boys in a class. A team of 10 players is to be selected from the class. What is the probability that a randomly chosen team includes 4 or 6 boys?

0.12
0.37
0.49
0.75

Answer 1

C

Explanation:

There are 6 girls and 7 boys in the class. 10 players can be selected in

`C^(13)_(10)=(13!)/(10!(13-10)!)=(11\cdot 12\cdot 13)/(2\cdot 3)=286`

different ways.

1. A team of 10 players with 4 boys includes 6 girls.

`C^7_4=(7!)/(4!(7-4)!)=(5\cdot 6\cdot 7)/(2\cdot 3)=35` - possible ways to choose 4 boys.

`C^6_6=(6!)/(6!(6-6)!)=1` - possible way to choose 6 girls.

2. A team of 10 players with 6 boys includes 4 girls.

`C^7_6=(7!)/(6!(7-6)!)=(7)/(1)=7` - possible ways to choose 6 boys.

`C^6_4=(6!)/(4!(6-4)!)=(5\cdot 6)/(2)=15` - possible ways to choose 4 girls.

3. The probability that a randomly chosen team includes 4 or 6 boys is

`Pr=(35\cdot 1+7\cdot 15)/(286)=(140)/(286)=(70)/(143)\approx 0.49.`