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

Question

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. 6
B. 9
C. 12
D. 36
E. 720

BrentGMATPrepNow · Accepted Answer

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:  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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chetan2u · Answer

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

Vinit800HBS · Answer

Assume that there are only 3 chairs for the boys to sit.
So they can be arranged in 3! Ways.

Now put 3 more chairs between 1st and 2nd boy, 2nd and 3rd boy ,and next to the 3rd boy.
So another 3! Ways..

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

Posted from my mobile device

RastogiSarthak99 · Answer

My 2 cents on this:

This question could easily be framed differently increasing the difficult, so be careful.

1st way --> whenever the word rearrangements/arrangements appear, I look at npr formulas. So, 3 boys have 3 seats available, hence 3! ways. Same for 3 Girls, 3 chairs, 3! ways. Total = 3! x 3! = 36 ways

2nd way: 3c1 x 3c1 x 2c1 x 2c1 x 1c1 x 1c1 (B,G,B,G,B) = 36 ways

Bunuel , what do you think of the 2nd way? Will it work in more complex questions?

QueenFreak · Answer

There are 3 girls and 3 boys and 6 seats, and two of the same gender can't sit together.

_ _ _ _ _ _
G B G B G B - Method 1
B G B G B G - Method 2

1 seat - 6 options
2 seat - 3 options ( B if G occupies 1 or vice versa) 
3 seat - 2 options ( B if G occupies 2 or vice versa)
4 seat - 2 options ( B if G occupies 3 or vice versa)
5 seat - 1 option   ( B if G occupies 4 or vice versa)
6 seat - 1 option   ( B if G occupies 5 or vice versa)

Total possible arrangements - 6*3*2*2*1*1 = 72 (D)

Answer - D

bumpbot · Answer

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

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