Question

A group of 6 is to be made out of 8 girls and 6 boys. What is the probability that exactly 3 boys are selected?

Answer 1

Answer:

(8C3 * 6C3) / 14C6

Step-by-step explanation:

exactly 3 boys will mean that the team has 3 girls and 3 boys.

choosing 3 girls from 8 = 8C3

choosing 3 boys from 6 = 6C3

total 6 people can be chosen from 8+6=14 people in 14C6 ways

Answer 2

Given,

• Total number of g-i-r-l-s = 8
• Total number of boys = 6

To find,

• We have to find the probability that exactly 3 boys are selected.

Solution,

We can simply find the probability that exactly 3 boys are selected by using the concept of permutations.

Total number of ways of selecting a group of 6 out of 8 g-i-r-l-s and 6 boys = ¹⁴C₆

Number of ways of selecting exactly three boys = ⁶C₃ * ⁸C₃

Probability = favorable outcomes / total  number of outcomes

P( that exactly 3 boys are selected) =  ⁶C₃ * ⁸C₃/ ¹⁴C₆

                                                           = 20 * 56 / 3003

                                                           = 1120/3003

Hence, a group of 6 is to be made out of 8 g-i-r-l-s and 6 boys, then the probability that exactly 3 boys are selected is 1120/3003.