10 men and 5 women are meeting in a conference room. Four people are chosen at random from the 15 to form a committee. (a) What is the probability that the committee consists of 2 men and 2 women? (b) Among the 15 is a couple, Bob and Jane. What is the probability that Bob and Jane both end up on the committee? (c) What is the probability that Bob ends up on the committee but Jane doesn’t?

Answer:Step-by-step explanation:GivenThere are 10 men and 5 women in a conference roomtotal People=15(a)Probability that the committee consists of 2 men and 2 womenwe have to select from 10 men and 5 women[tex]P=\frac{^5C_2\times ^{10}C_2}{^{15}C_4}[/tex](b)Bob and Jane end up on the same committee as bob and Jane are necessary to include so there are 4 women and 9 men left to select remaining 2 person[tex]P=\frac{^{13}C_2}{^{15}C_4}[/tex](c)Bob is in the committee but Jane is not9 men and 4 women left to choose other 3 person[tex]P=\frac{^{13}C_3}{^{15C_4}}[/tex]