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 10 men and 8 women. a) In how many ways can Alina select the 10 other players? 43758 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? 6720 c) Suppose that, in addition to the restrictions posed in part b), Cody (one of the men Alina must select from) refuses to join the team. Now in how many ways can Alina choose the 10 remaining players? d) Suppose that, in addition to the restrictions posed in parts b) and c), Tyler (one of the men Alina must select from) will join the team if and only if Sam (another one of the men Alina must select from) joins. Now in how many ways can Alina choose the 10 remaining 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

d)Now Alina has 10 men and 8 women of which Tyler joins only if Sam joins and Cody doesnt join

So Ways=2016-N(None of Sam and Tyler Join)=2016-7C7*8C3=1960

e)Now we have 10 men and 8 women but Matt and Jenn refuse to play together.

Hece Ways=6720-N(Both Matt and Jenn play)=6720-9C6*7C2=4956

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