Answer:
[tex]165,20,\frac{4}{33}[/tex]
Step-by-step explanation:
GIVEN: A group consists of five men and six women. Three people are selected to attend a conference.
TO FIND: a) In how many ways can three people be selected from this group of eleven. b) In how many ways can three women be selected from the six women. c) Find the probability that the selected group will consist of all women.
SOLUTION:
a)
Total ways in which three people be selected from this group of eleven is
[tex]=11C_{3}=\frac{11!}{8!3!}[/tex]
[tex]=165[/tex]
b)
Total ways in which three women can be selected from the six women
[tex]=6C_{3}=\frac{6}{3!3!}[/tex]
[tex]=20[/tex]
c)
Probability that the selected group will consist of all women
[tex]=\frac{\text{total ways in which three women can be selected}}{\text{total ways of selection}}[/tex]
[tex]=\frac{6C_3}{11C_3}[/tex]
[tex]=\frac{20}{165}=\frac{4}{33}[/tex]
