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Coach Jackson will choose at least two players for his team

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by Gmat_mission » Sun Jun 30, 2019 9:24 am

Timer

00:00

Answers

A

B

C

D

E

Stats

Difficulty—

Coach Jackson will choose at least two players for his team from those who try out on Saturday. How many players will Coach Jackson choose?

(1) Coach Jackson could choose exactly 20 different teams.
(2) At least two players at the tryout will not be chosen.

[spoiler]OA=C[/spoiler]

Source: Princeton Review
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by Ian Stewart » Mon Jul 01, 2019 6:16 am
I have no idea what this question is even asking. From the stem, the coach is choosing "two players *for* his team", and then Statement 1 talks about the total number of teams he can choose. Is he choosing his complete team on Saturday? Or just part of it? If just part of it, when he chooses the rest of his team, what restrictions do we have?

If you assume he's picking his entire team on Saturday, and there are 20 different teams he can choose, then if he must pick at least two players, he is either picking 3 out of 6 tryouts (6C3 = 6*5*4/3! = 20) or he is picking 19 out of 20 tryouts (20C19 = 20). Statement 2 rules out the second possibility, so the answer would be C. But as the question is worded, the answer is E, because there's no way to know what this coach is even doing.
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