board member question #2

Question

There are eight female board members and twenty-two male board members.

How many ways are there to make a committee of ten board members?

1. __________ways

How many ways are there to make a committee of ten board members if exactly three must be female?

1. __________ways

Determine the probability of selecting a committee of ten board members where exactly three of the members were female. Write your answer as a decimal, rounded to the nearest thousandth.

1. Answer: __________

Answer 1

There is a total of 30 people to choose from and you want to pick any ten. This is the combination of 30 items take 10 at a time: ₃₀C₁₀ = 30,045,015.

To form a committee of exactly three women, there are eight women to choose from: ₈C₃ = 56. Each of those possibilities can be paired with seven possible men combis: ₂₂C₇= 170,544. According to the fundamental counting principle if there are m ways to do taek1 and n ways to do task2, there are m X n ways to do both. So the possible number of committees with 3 women is 56(170,544)= 9,550.464.

To get the probability of that committee divide that number by the total possible number of outcomes (determined in first part).

₈C₃·₂₂C₇/ ₃₀C_10.

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