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How many different ways are there to arrange . . .

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by M7MBA » Sun Dec 10, 2017 10:21 am
How many different ways are there to arrange a group of 3 adults and 4 children in 7 seats if adults must have the first, third, and 7 seats?

A. 12
B. 144
C. 288
D. 1,400
E. 5,040

The OA is B.

Can any expert give me a detailed explanation of how can I solve this PS question? Thanks.
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by EconomistGMATTutor » Sun Dec 10, 2017 11:36 am
Hello M7MBA.

We have to arrange 3 adults and 4 children in 7 seats in the following form: A C A C C C A.

For the first place, we have 3 options.
For the second place, we have 4 options.
For the third place, we have 2 options.
For the fourth place, we have 3 options.
For the fifth place, we have 2 options.
For the sixth place, we have 1 option.
For the seventh place, we have 1 option.

So, the total of options to arrange the 7 people is equal to 3*4*2*3*2*1*1 = 144.

So, the correct answer is B.

I hope this explanation may help you.

Feel free to ask me again if you have a doubt.

Regards.
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by GMATWisdom » Sun Dec 10, 2017 12:42 pm
M7MBA wrote:How many different ways are there to arrange a group of 3 adults and 4 children in 7 seats if adults must have the first, third, and 7 seats?

A. 12
B. 144
C. 288
D. 1,400
E. 5,040

The OA is B.

Can any expert give me a detailed explanation of how can I solve this PS question? Thanks.
three adults can be placed in three seats in 3! ways = 3*2*!=6
four children can be placed in four seats in 4! ways =4*3*2*1=24
Hence total number of ways = 6*24= 144
So B is the correct option.
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by Scott@TargetTestPrep » Fri Sep 27, 2019 7:36 am
M7MBA wrote:How many different ways are there to arrange a group of 3 adults and 4 children in 7 seats if adults must have the first, third, and 7 seats?

A. 12
B. 144
C. 288
D. 1,400
E. 5,040

The OA is B.

Can any expert give me a detailed explanation of how can I solve this PS question? Thanks.
The 3 adults can be arranged in 3! = 6, and the 4 children can be arranged in 4! = 24 ways, so the total number of arrangements is 6 x 24 = 144.

Answer: B

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