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. in how many ways can Alina select the 10 other players? 184756 Suppose now that, of the 10 remaining players, there must be exactly 6 men and 4 women. in how many ways can Alina select the 10 other players? 58212 Suppose that, in addition to the restrictions posed in part 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? 26460 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? 19404 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

a)

20C10=184756

b)

11C6*9C4=58212

c)

10C6*9C4=26460

d)

1C1*9C5*9C4 (Sam and Tyler both join)

OR

9C6*9C4 (Only Sam joins)

OR

8C6*9C4 (Neither joins)

=15876+10584+3528=29988

e)

10C6*8C4 (Matt joins and Jenn doesn’t)

OR

9C6*9C4 (Jenn joins and Matt doesn’t)

14700+10584=25284

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