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A septet, a group composed of seven players, is made up of

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A septet, a group composed of seven players, is made up of [#permalink] New post 08 Oct 2017, 22:44
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A septet, a group composed of seven players, is made up of four strings and three woodwind instruments. If seven students try out for strings and seven different students try out for woodwinds, how many unique septets can result?

(A) 35
(B) 70
(C) 210
(D) 420
(E) 1225



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Re: A septet, a group composed of seven players, is made up of [#permalink] New post 09 Oct 2017, 02:04
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Bunuel wrote:
A septet, a group composed of seven players, is made up of four strings and three woodwind instruments. If seven students try out for strings and seven different students try out for woodwinds, how many unique septets can result?

(A) 35
(B) 70
(C) 210
(D) 420
(E) 1225



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Here we need to choose 4 strings out of 7 and 3 woodwind out of 7

i.e 7C4 * 7C3

= 35 * 35 =1225
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Re: A septet, a group composed of seven players, is made up of [#permalink] New post 02 Jan 2018, 09:23
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Bunuel wrote:
A septet, a group composed of seven players, is made up of four strings and three woodwind instruments. If seven students try out for strings and seven different students try out for woodwinds, how many unique septets can result?

(A) 35
(B) 70
(C) 210
(D) 420
(E) 1225


The number of ways to select the 4 strings is 7C4 = 7!/[4!(7-4)!] = (7 x 6 x 5 x 4)/4! = (7 x 6 x 5 x 4)/(4 x 3 x 2) = 7 x 5 = 35.

The number of ways to select the 3 woodwinds is 7C3 = 7!/[3!(7-3)!] = (7 x 6 x 5)/3! = (7 x 6 x 5)/(3 x 2) = 7 x 5 = 35.

Thus, the total number of ways to select the group is 35 x 35 = 1,225.

Answer: E
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Re: A septet, a group composed of seven players, is made up of   [#permalink] 02 Jan 2018, 09:23
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