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

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A septet, a group composed of seven players, is made up of four string  [#permalink]

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New post 17 Aug 2017, 01:13
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Question Stats:

80% (01:45) correct 20% (01:53) wrong based on 109 sessions

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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 four string  [#permalink]

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New post 17 Aug 2017, 02:09
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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


7C4*7C3 = 35*35 = 1225

Answer: option E
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Re: A septet, a group composed of seven players, is made up of four string  [#permalink]

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New post 17 Aug 2017, 02:17
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


7C4 * 7C3 = 35 * 35 = 1225
E
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Re: A septet, a group composed of seven players, is made up of four string  [#permalink]

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New post 24 Aug 2017, 13:46
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 four string   [#permalink] 24 Aug 2017, 13:46
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