A four-person committee is chosen from a group of eight boys and six girls.

If students are chosen at random, what is the probability that the committee consists of all boys?

1001

15

1001

10

143

133

143

Answer: 70/1001

Step-by-step explanation:

Choosing 4 boys from total of 8 boys is a combination of 8 when 4 is taken at a time:

8C4 = 8!/4!4!

= 70

Since they are all boys, that means we are choosing 0 girl from the 6 girls.

6C0 = 6!/6!0!

= 1

Choosing 4 students from a total of 6+8=14 students is a combination of 14 when 4 people is taken at a time:

14C4 = 14!/10!4!

= 1001

This will give a probability of:

(70 * 1) / 1001

= 70/1001

30.3%

Step-by-step explanation:

To find the probability of all people in the committee being boys, we have:

First person boy: 8 boys among 14 people: P1 = 8/14 = 4/7

Second person boy: 7 boys among 13 people: P1 = 7/13

Third person boy: 6 boys among 12 people: P1 = 6/12 = 1/2

Fourth person boy: 5 boys among 11 people: P1 = 5/11

So the final probability is:

(4/7) * (7/3) * (1/2) * (5/11) = (4*7*5) / (7*3*2*11) = (2*5) / (3*11) = 10/33 = 0.303 = 30.3%