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3 girls and 4 boys line up in a row. If girls stand at the first and b

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3 girls and 4 boys line up in a row. If girls stand at the first and boys stand at the last, how many possible cases are there?

A. 96
B. 108
C. 144
D. 192
E. 256
[Reveal] Spoiler: OA

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New post 14 Sep 2017, 02:00
Since the girls stand in the front and the boys stand in the back,
the arrangement must be of the form G-G-G-B-B-B-B

There are 3 ways in which the first position in the row is filled with a girl,
2 ways of filling the 2nd position with a girl and only one way of filling the third position.
A similar process is followed by which the boys are positioned in the row.

Total ways of forming the line are \(3*2*1*4*3*2*1 = 2^2*3^2*4 = 4*9*4 = 144\)(Option C)
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Re: 3 girls and 4 boys line up in a row. If girls stand at the first and b [#permalink]

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New post 17 Sep 2017, 18:44
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The number of ways that 3 girls permute is 3! = 6 and the number of ways that 4 boys permute is 4! = 24. Those cases happen together and so the number of cases that 3 girls stand at the first and 4 boys stand at the last is 3! * 4! = 6 * 24 = 144.

Ans: C
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Re: 3 girls and 4 boys line up in a row. If girls stand at the first and b   [#permalink] 17 Sep 2017, 18:44
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