As its star player, Alina becomes the captain of the Applied Math soccer team an

Question

As its star player, Alina becomes the captain of the Applied Math soccer team and is tasked with choosing the 10 other players from a set of

11 men and 9 women.

b) Suppose now that, of the 10 remaining players, there must be exactly 7 men and 3 women. In how many ways can Alina select the 10 other players?

e )Suppose that, in addition to the restrictions posed in part b), Matt (one of the men Alina must select from) and Jenn (one of the women Alina must select from) refuse to play for the same team. In how many ways can Alina choose the 10 remaining players?

Explanation / Answer

b) The number of ways selecting 7 men and 3 women out 11 men and 9 women is

11C7 * 9C3 = 330*84 =27720 ways

e) Matt and Alina must select. So if they are selected then the remaming 6 mean and 2 women can be selected out of 10 mean and 8 momen is 10C6 * 8C2 = 210*28 =5880 ways

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