9 A company claimed to randomly choose a committee of three

9. A company claimed to randomly choose a committee of three employees to represent the employees at a bargaining session. Of the 50 employees from whom the committee was chosen, 20 are female and 30 are male. The committee turned out to be all male. a) Determine the number of ways a committee of three can be chosen out of the 50 employees. b) Determine the number of ways a committee of three can be chosen out of the 30 male employees. c) Determine the probability the committee of three would be all male, if the selection were truly random. d) Determine the probability the committee of three would include at least one female, if the selection were truly random.

Solution

a) 50C3

b) 30C3

c) 30C3/50C3

d) P(2 males, 1 female)+P(1 male, 2 females)+P(3 females)

= 1-P(all males)

=1-(30C3/50C3)