probability question

Question

A TV studio has brought in 

8

 boy kittens and 6

 girl kittens for a cat food commercial.

The director is going to choose 7

 of these kittens at random to be in the commercial.What is the probability that the director chooses 3

 boy kittens and 4

 girl kittens? Round your answer to three decimal places.

Answer 1

Jaimie,

There are 14 kittens all together, 8 of which are male and 6 female.

The sample space is C(14,7) as they will choose 7 out of 14 kittens.

The favorable outcome is to have 3 boys and 4 girls, which can occur in C(8,3)*C(6,4) different ways.

C(8,3)*C(6,4) 840

So the probability is p= --------------------- = --------- = 0.244755 -> 0.245 =24.5%

C(14,7) 3432