Question

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

Answer 1

Answer:

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%

Answer 2

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