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In how many arrangements can a teacher seat 3 girls and 3 bo

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In how many arrangements can a teacher seat 3 girls and 3 bo [#permalink]

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In how many arrangements can a teacher seat 3 girls and 3 boys in a row of 6 seats if no two children of the same gender are to be adjacent?

(A) 6
(B) 12
(C) 36
(D) 72
(E) 144
[Reveal] Spoiler: OA

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Re: In how many arrangements can a teacher seat 3 girls and 3 bo [#permalink]

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New post 22 Aug 2013, 10:27
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Asifpirlo wrote:
In how many arrangements can a teacher seat 3 girls and 3 boys in a row of 6 seats if no two children of the same gender are to be adjacent?

(A) 6
(B) 12
(C) 36
(D) 72
(E) 144


BGBGBG or GBGBGB --> 2 ways,

Both 3 B's and 3 G's can be arranged in 3! ways.

Thus toal 2*3!*3!=72.

Answer: D.
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Re: In how many arrangements can a teacher seat 3 girls and 3 bo [#permalink]

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New post 01 Jan 2015, 17:02
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Hi All,

These types of story-based permutation questions can usually be solved with a basic drawing and some multiplication.

Here, we're told to sit 6 children in a row (3 boys and 3 girls) and that two adjacent seats CANNOT have the same gender. We're asked for the total number of possible ways to seat the 6 children.

So, let's start with 6 chairs:

_ _ _ _ _ _

The first chair can have ANY of the children:

6 _ _ _ _ _

Whether you put a boy or a girl in that first chair, the second chair MUST have the opposite gender - there will be 3 of those children available:

6 3 _ _ _ _

From here, we just have to go "back and forth" with the 2 remaining boys and the 2 remaining girls:

6 3 2 2 1 1

Now, we just multiply the numbers: (6)(3)(2)(2)(1)(1) = 72 possible arrangements

Final Answer:
[Reveal] Spoiler:
D


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Re: In how many arrangements can a teacher seat 3 girls and 3 bo [#permalink]

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New post 12 Jan 2015, 00:31
B G B G B G=3*3*2*2*1*1

OR

G B G B G B=3*3*2*2*1*1

36+36=72

D

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Re: In how many arrangements can a teacher seat 3 girls and 3 bo [#permalink]

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New post 06 Oct 2017, 05:24
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Re: In how many arrangements can a teacher seat 3 girls and 3 bo   [#permalink] 06 Oct 2017, 05:24
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