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A teacher wants to select a team of 5 players from a group

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A teacher wants to select a team of 5 players from a group

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A teacher wants to select a team of 5 players from a group of 9 players. However, she needs to keep the following constraints in mind: If Jane is in the team, Sue should also be included in the team and vice versa.

In how many ways can the teacher select the team for a tournament?

A) 21
B) 35
C) 56
D) 120
E) 126

OA=D

Source: e-GMAT

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Hi VJesus12,

We're told that a teacher wants to select a team of 5 players from a group of 9 players. However, she needs to keep the following constraints in mind: If Jane is in the team, Sue should also be included in the team and vice versa. We're asked for the number of different ways that the teacher can select the team for a tournament. This question is a Combination Formula question with a 'twist': you either need BOTH girls on the team OR you need NEITHER girl on the team. Those two options require slightly different calculations.

Combination Formula = N!/K!(N-K)! where N is the total number of people and K is the size of the subgroup.

For Jane and Sue to be on the team, those two players would take 2 of the 5 'spots', so the other 3 spots would be chosen from the remaining 7 players...
7!/3!(7-3)! = (7)(6)(5)/(3)(2)(1) = 35 options

For NEITHER Jane NOR Sue to be on the team, the 5 'spots' would be chosen from the other 7 players...
7!/5!(7-5)! = (7)(6)/(2)(1) = 21 options

Total possible teams = 35 + 21 = 56

Final Answer: C

GMAT assassins aren't born, they're made,
Rich

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Contact Rich at Rich.C@empowergmat.com

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