Question

A 4-person leadership committee is randomly chosen from a group of 24 candidates. Ten of the candidates are men, and 14 are women.
What is the probability that the committee is all male or all female?
What is the probability that the committe has at least 1 man or at least 1 women?

Answer 1

All male probability: 10/24*9/23*8/22*7/21 = 5040/255,024
= 0.01976

All female probability:
14/24*13/23*12/22*11/21= 24,024/255,024
= 0.09420

prob. of at least one man and one woman:

= 1 - (prob. of zero males) - (prob. of zero females) = 1- 0.01976 - 0.09420
= 0.88604