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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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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BTGmoderatorDC
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Solution:BTGmoderatorDC wrote: ↑Tue Aug 11, 2020 7:09 pmSeven 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
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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