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In how many arrangements can a teacher seat 3 girls and 3 boys in a

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

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New post 16 Apr 2017, 22:59
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In how many arrangements can a teacher seat 3 girls and 3 boys in a row of 6 seats if the boys are to have the first, third, and fifth seats?

A. 3
B. 6
C. 9
D. 18
E. 36
[Reveal] Spoiler: OA

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

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New post 17 Apr 2017, 07:07
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Bunuel wrote:
In how many arrangements can a teacher seat 3 girls and 3 boys in a row of 6 seats if the boys are to have the first, third, and fifth seats?

A. 3
B. 6
C. 9
D. 18
E. 36


Take the task of seating the 6 students and break it into stages.

NOTE: Since the boys must sit in seats 1, 3 and 5, the girls must sit in seats 2, 4 and 6

Stage 1: Select a boy to sit in seat #1
We can choose any of the 3 boys, so we can complete stage 1 in 3 ways

Stage 2: Select a girl to sit in seat #2
We can choose any of the 3 girls, so we can complete stage 2 in 3 ways

Stage 3: Select a boy to sit in seat #3
There are 2 boys remaining to be seated, so we can complete stage 3 in 2 ways

Stage 4: Select a girl to sit in seat #4
There are 2 girls remaining to be seated, so we can complete stage 4 in 2 ways

Stage 5: Select a boy to sit in seat #5
There is 1 boy remaining to be seated, so we can complete stage 5 in 1 way

Stage 6: Select a girl to sit in seat #6
There is 1 girl remaining to be seated, so we can complete stage 6 in 1 way

By the Fundamental Counting Principle (FCP), we can complete all 6 stages (and thus seat all 6 children) in (3)(3)(2)(2)(1)(1) ways (= 36 ways)

Answer:
[Reveal] Spoiler:
E


Note: the FCP can be used to solve the MAJORITY of counting questions on the GMAT. So, be sure to learn it.

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

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New post 17 Apr 2017, 07:14
Bunuel wrote:
In how many arrangements can a teacher seat 3 girls and 3 boys in a row of 6 seats if the boys are to have the first, third, and fifth seats?

A. 3
B. 6
C. 9
D. 18
E. 36



Another method could be..

3 boys are in 1st, 3rd and 5th position, so they can be arranged in 3! Ways.
3 girls are in remaining THREE positions, so another 3! Ways..

Each positioning of boys will have 3! Ways of positioning girls
So total ways = 3!*3!=6*6=36

E
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Re: In how many arrangements can a teacher seat 3 girls and 3 boys in a   [#permalink] 17 Apr 2017, 07:14
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