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In how many different ways, can a coach select a team of 3 players out

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In how many different ways, can a coach select a team of 3 players out [#permalink] New post   28 Apr 2020, 20:28
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In how many different ways, can a coach select a team of 3 players out of 10 players so that John, who is one among the 10 players, is selected in the team?

A) 6
B) 9
C) 12
D) 18
E) 36
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E
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In how many different ways, can a coach select a team of 3 players out [#permalink] New post   28 Apr 2020, 21:57
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John is always selected so from rest 9 we have to select 2
thus
9C2 = 36
E
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Re: In how many different ways, can a coach select a team of 3 players out [#permalink] New post   28 Apr 2020, 22:46
Since John is already selected, we have to selected only two more persons from 9. Therefore the answer is 9C2 = 36.

Option E is the correct answer.
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Re: In how many different ways, can a coach select a team of 3 players out [#permalink] New post   29 Apr 2020, 04:19
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A team of 3 players needs to be selected in which John is definitely going to be there. So, effectively, only two players have to be selected from 9 players.

Number of ways of selecting ANY 2 players out of 9 players = \(9_C_2\) = 9 * 8 / 2 = 36 ways.
The correct answer option is E.

Of n objects, if r objects have to be selected such that ‘x’ objects should always be a part of the selection, the number of ways of doing this = \((n-x)_C_(r-x)\)
Hope that helps!
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Re: In how many different ways, can a coach select a team of 3 players out [#permalink] New post   20 May 2021, 07:48
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We don't have to select John, as he will be always on the team.

The remaining 2 players will be selected out of 9 available players: \(^9{C_2} = 36\)

Answer E
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Re: In how many different ways, can a coach select a team of 3 players out [#permalink] New post   31 Aug 2022, 03:47
@buenel . Can we do this by table method or any other method?
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Re: In how many different ways, can a coach select a team of 3 players out [#permalink]
31 Aug 2022, 03:47
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