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Seven children — A, B, C, D, E, F, and G — are going to sit in seven chairs in a row. The children C & F have to sit

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Seven children — A, B, C, D, E, F, and G — are going to sit in seven chairs in a row. The children C & F have to sit

by BTGmoderatorDC » Tue Aug 11, 2020 7:09 pm

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Seven children — A, B, C, D, E, F, and G — are going to sit in seven chairs in a row. The children C & F have to sit next to each other, and the others can sit in any order in any remaining chairs. How many possible configurations are there for the children?

A. 600
B. 720
C. 1440
D. 4320
E. 4800


OA C

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Re: Seven children — A, B, C, D, E, F, and G — are going to sit in seven chairs in a row. The children C & F have to sit

by Scott@TargetTestPrep » Sat Aug 15, 2020 4:00 am
BTGmoderatorDC wrote: ↑
Tue Aug 11, 2020 7:09 pm
 Seven children — A, B, C, D, E, F, and G — are going to sit in seven chairs in a row. The children C & F have to sit next to each other, and the others can sit in any order in any remaining chairs. How many possible configurations are there for the children?

A. 600
B. 720
C. 1440
D. 4320
E. 4800


OA C

Solution:

Since children C and F must always sit next to each other, we can consider them as a single entity [C-F]. We can express the row of children as follows:

[C-F][A][D][E][G]

We see that there are 6 slots which can be arranged in 6! = 720 ways.

We also have to account for the number of ways to arrange C-F, which is 2!, so the total number of arrangements is 1,440.


Answer: C

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