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The local orchestra is holding tryouts. Six violinists are competing

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The local orchestra is holding tryouts. Six violinists are competing [#permalink]

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New post 08 Apr 2016, 02:56
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The local orchestra is holding tryouts. Six violinists are competing for 2 positions, 5 pianists are competing for 1 position, and 8 trombonists are competing for 4 positions. If Suzette and Monica are 2 of the 8 trombonists and if the two women can never be in the orchestra together, how many different personnel configurations for the orchestras are possible?

A. 4,125
B. 4,150
C. 4,175
D. 4,200
E. 4,225
[Reveal] Spoiler: OA

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Re: The local orchestra is holding tryouts. Six violinists are competing [#permalink]

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New post 08 Apr 2016, 21:40
Total number of ways of selecting the local orchestra = 6C2 * 5C1 * 8C4

Number of ways of selecting the orchestra by having both Suzette and Monica = 6C2 * 5C1 * 6C2

Number of ways of selecting the orchestra such that Suzette and Monica are not together = 6C2 * 5C1 (8C4 - 6C2) = 75 * 55 = 4125

Answer: A

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Re: The local orchestra is holding tryouts. Six violinists are competing [#permalink]

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New post 09 Apr 2016, 07:09
Vyshak wrote:
Total number of ways of selecting the local orchestra = 6C2 * 5C1 * 8C4

Number of ways of selecting the orchestra by having both Suzette and Monica = 6C2 * 5C1 * 6C2

Number of ways of selecting the orchestra such that Suzette and Monica are not together = 6C2 * 5C1 (8C4 - 6C2) = 75 * 55 = 4125

Answer: A



Hi

Please tell the difference between yours and mine approach

6C2.5C1(6C4 + 2C1.7C3)

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The local orchestra is holding tryouts. Six violinists are competing [#permalink]

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New post 09 Apr 2016, 07:22
RatneshS wrote:
Vyshak wrote:
Total number of ways of selecting the local orchestra = 6C2 * 5C1 * 8C4

Number of ways of selecting the orchestra by having both Suzette and Monica = 6C2 * 5C1 * 6C2

Number of ways of selecting the orchestra such that Suzette and Monica are not together = 6C2 * 5C1 (8C4 - 6C2) = 75 * 55 = 4125

Answer: A



Hi

Please tell the difference between yours and mine approach

6C2.5C1(6C4 + 2C1.7C3)


Hi,

In your approach you have selected either Suzette or Monica (2C1) which is fine. However you have chosen 7 members(7C3) when there are only 6 members remaining, resulting in a wrong answer. 2C1 * 6C3 should provide you the correct answer.

In your approach the correct answer should be read as: 6C2.5C1(6C4 + 2C1.6C3)

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Re: The local orchestra is holding tryouts. Six violinists are competing [#permalink]

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New post 10 Sep 2017, 11:20
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Re: The local orchestra is holding tryouts. Six violinists are competing   [#permalink] 10 Sep 2017, 11:20
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