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

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Senior Manager
Joined: 10 Jul 2013
Posts: 318
In how many arrangements can a teacher seat 3 girls and 3 bo  [#permalink]

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22 Aug 2013, 11:18
2
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Difficulty:

45% (medium)

Question Stats:

57% (00:52) correct 43% (00:37) wrong based on 201 sessions

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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

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Asif vai.....

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Joined: 02 Sep 2009
Posts: 47157
Re: In how many arrangements can a teacher seat 3 girls and 3 bo  [#permalink]

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22 Aug 2013, 11:27
2
1
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.

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

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01 Jan 2015, 18:02
1
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.

_ _ _ _ _ _

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

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

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12 Jan 2015, 01:31
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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Joined: 09 Sep 2013
Posts: 7312
Re: In how many arrangements can a teacher seat 3 girls and 3 bo  [#permalink]

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