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The editor of an anthology of short stories has to select authors from

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GMAT Forum Moderator
Joined: 28 May 2014
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GMAT 1: 730 Q49 V41
The editor of an anthology of short stories has to select authors from [#permalink]

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01 Feb 2018, 03:20
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33% (00:00) correct 67% (01:04) wrong based on 12 sessions

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The editor of an anthology of short stories has to select authors from a pool of 12 authors, of which 4 are female. If the anthology is to include the work of 8 authors of which at least 2 must be female, in how many ways can the editor select the authors?

A) 168
B) 201
C) 294
D) 462
E) 495
[Reveal] Spoiler: OA

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The editor of an anthology of short stories has to select authors from [#permalink]

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01 Feb 2018, 08:02
saswata4s wrote:
The editor of an anthology of short stories has to select authors from a pool of 12 authors, of which 4 are female. If the anthology is to include the work of 8 authors of which at least 2 must be female, in how many ways can the editor select the authors?

A) 168
B) 201
C) 294
D) 462
E) 495

If we need to include 8 authors where a minimum of 2 authors have to be female,
there are 3 ways we can choose the authors.

Case 1: 2 female authors and 6 male authors
$$C^2_4 * C^6_8 = 6*28 = 168$$

Case 2: 3 female authors and 5 male authors
$$C^3_4 * C^5_8 = 4*56 = 224$$

Case 3: 4 male and female authors
$$C^4_4 * C^4_8 = 1*70 = 70$$

Therefore, the total ways in which the editor can select the authors are 462(168+224+70) (Option D)
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Re: The editor of an anthology of short stories has to select authors from [#permalink]

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01 Feb 2018, 08:28
Total number of ways to select 8 authors from 12 = 12C8 = 495

Number of ways to select 8 authors having less than 2 female authors = 8C7 * 4C1 + 8C8 = 32 + 1 = 33

Number of ways the editor can select 8 authors of which atleast 2 are female = 495 - 33 = 462

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Re: The editor of an anthology of short stories has to select authors from [#permalink]

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02 Feb 2018, 12:17
saswata4s wrote:
The editor of an anthology of short stories has to select authors from a pool of 12 authors, of which 4 are female. If the anthology is to include the work of 8 authors of which at least 2 must be female, in how many ways can the editor select the authors?

A) 168
B) 201
C) 294
D) 462
E) 495

We can use the formula:

Number of ways to select at least two female authors = Total number of ways to select the authors - number of ways to select 1 female author or no female authors

The total number of ways to select 8 authors among 12 is 12C8:

12C8 = 12!/[(12 - 8)! x 8!] = (12 x 11 x 10 x 9)/4! = (12 x 11 x 10 x 9)/(4 x 3 x 2 x 1) = 11 x 5 x 9 = 495

The number of ways to select exactly 1 female author is:

4C1 x 8C7 = 4 x 8 = 32

The number of ways to select no female authors is :

4C0 x 8C8 = 1 x 1 = 1

Thus, the number of ways to select at least two female authors is:

495 - 32- 1 = 462

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Re: The editor of an anthology of short stories has to select authors from   [#permalink] 02 Feb 2018, 12:17
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