Respuesta :
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]
