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A certain musical piece is to be played by an equal number of

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A certain musical piece is to be played by an equal number of  [#permalink]

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New post 04 Sep 2018, 23:24
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A certain musical piece is to be played by an equal number of violinists and cellists. If there are 6 violinists and 2 cellists available to play the piece, how many different groups of musicians could be selected to play the piece?

(A) 12
(B) 15
(C) 27
(D) 28
(E) 70
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A certain musical piece is to be played by an equal number of  [#permalink]

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New post 05 Sep 2018, 00:40
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You will have those combinations
If cellist = 1 -> 2*1C6 ways to choose violist as 2 ways to choose cellist
if cellist = 2 -> 2C6 = 15 ways to choose violist
=> Total = 27
OA C
Expert please helps me to correct, whether my approach is right? Thanks so much
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Re: A certain musical piece is to be played by an equal number of  [#permalink]

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New post 27 Jan 2019, 14:32
Bismarck wrote:
A certain musical piece is to be played by an equal number of violinists and cellists. If there are 6 violinists and 2 cellists available to play the piece, how many different groups of musicians could be selected to play the piece?

(A) 12
(B) 15
(C) 27
(D) 28
(E) 70


The trap to avoid here is assuming that "an equal number" automatically means two, while it could actually be 1 or 2 violinists/cellists. But technically, couldn't it mean 0 of each too? I guess if there's 0 of each they're not playing the piece at all, but at the same time 6C0*2C0 would be 1*1 which would add +1 to the total number of possibilities, which would be 28 instead of 27. Please correct me if I'm wrong...am I just over analyzing this?
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Re: A certain musical piece is to be played by an equal number of   [#permalink] 27 Jan 2019, 14:32
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