Question

A group consists of five men and five women. Three people are selected to attend a conference.
A. In how many ways can three people be selected from this group of ten?
B. In how many ways can three women be selected from the five women?
C. Find the probability that the selected group will consist of all women.

Answer 1

Answer:

a) 120

b) 10

c) 1/12

Step-by-step explanation:

The number of ways that a sample of r can be selected from a population of n is:

nCr = n! / (r! (n−r)!)

a) 3 people selected from a group of 10

₁₀C₃ = 120

b) 3 women selected from a group of 5

₅C₃ = 10

c) Of the 120 committees that can be chose, 10 are all women.  So the probability is 10/120 = 1/12.