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

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Re: In how many different ways, can a coach select a team of 3 players out [#permalink]
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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]
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: $$^9{C_2} = 36$$