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 7 women.

a) In how many ways can Alina select the 10 other players?

b) 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?

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

A) total players=11+7=18 from that 10 should be selected

Ans:18C10=43758.

B)6men and 4 women so

11C6*7C4=16170.

C)As cody refused there are only 10 options remaining for her keeping same restrictions

10C6*7C4=7350.

D)Remove Sam so automatically tyler is removed so only 8 boys remaining

So 8C6*7C4=980 ->1

Include Sam guarantee So tyler is ready for selection he may be selected or may not be

if tyler is also selected

2 are selected before only from remaining 8men 4 men are to be selected(Remember Cody Refused in b)

So, 8C4*7C4=2450 ->2

Tyler is left out

5 more men needed from 8

8C5*7C4=1960 ->3

Adding 1&2&3 we get total ways=980+2450+1960=5390ways.

E)Matt and Jenn Refuse to play in one Team

Case-1:Matt In and Jenn Out:

9C5*6C4=1890

Case-2:Matt out and Jenn In.

9C6*6C3=1680

Case-3:Both matt and Jenn out

9C6*7C4=2940

Total=1890+1680+2940=6510 ways

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