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A certain play is to be performed with an equal number of male and fem

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A certain play is to be performed with an equal number of male and fem  [#permalink]

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New post 03 Feb 2017, 04:17
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Question Stats:

59% (00:54) correct 41% (00:52) wrong based on 88 sessions

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A certain play is to be performed with an equal number of male and female actors. If 2 different male actors and 5 different female actors are available to perform, how many different combinations of actors could be chosen to perform the play?

(A) 10
(B) 20
(C) 30
(D) 40
(E) 50

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Re: A certain play is to be performed with an equal number of male and fem  [#permalink]

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New post 08 Feb 2017, 19:38
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SajjadAhmad wrote:
A certain play is to be performed with an equal number of male and female actors. If 2 different male actors and 5 different female actors are available to perform, how many different combinations of actors could be chosen to perform the play?

(A) 10
(B) 20
(C) 30
(D) 40
(E) 50


We have two scenarios in which the same number of males and females will be selected to perform in the play.

Scenario #1:

1 male and 1 female performer:

We can select the male performer in 2C1 = 2 ways

We can select the female performer in 5C1 = 5 ways

Thus, we can select 1 male and 1 female performer in 2 x 5 = 10 ways.

Scenario #2:

2 male and 2 female performers:

We can select the 2 male performers in 2C2 = 1 way

We can select the 2 female performers in 5C2 = (5 x 4)/2! = 10 ways

Thus, we can select 2 male and 2 female performers in 1 x 10 = 10 ways.

Thus, we can select an equal number of male and female performers in 10 + 10 = 20 ways.

Answer: B
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Re: A certain play is to be performed with an equal number of male and fem  [#permalink]

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New post 21 Apr 2017, 15:49
agree with the above statement.
we can have 1 male 1 female or 2 males and 2 females.
2C1 * 5C1 = 2*5 = 10
2C2 * 5C2 = 1*10 = 10
total: 10+10 = 20.
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Re: A certain play is to be performed with an equal number of male and fem  [#permalink]

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New post 21 Apr 2017, 23:27
If we choose a combination of 1 male and 1 female then there are

2c1 and 5c1 = 2 x 5 = 10 ways


If we choose a combination of 2 males and 2 females then there are

2c2 and 5c2= 2 x 5= 10 ways

10 + 10= 20 ways.
Re: A certain play is to be performed with an equal number of male and fem &nbs [#permalink] 21 Apr 2017, 23:27
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