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Alice, Bob, Cindy, Darren, Eddie, Fabian sit on six chairs a

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by Max@Math Revolution » Mon Mar 11, 2019 4:56 pm

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[GMAT math practice question]

Alice, Bob, Cindy, Darren, Eddie, Fabian sit on six chairs around a large round table. Alice must sit opposite Bob and Cindy must sit opposite Darren. How many seating arrangements are possible?

A. 6
B. 8
C. 24
D. 120
E. 720
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by GMATGuruNY » Tue Mar 12, 2019 3:03 am
Max@Math Revolution wrote:[GMAT math practice question]

Alice, Bob, Cindy, Darren, Eddie, Fabian sit on six chairs around a large round table. Alice must sit opposite Bob and Cindy must sit opposite Darren. How many seating arrangements are possible?

A. 6
B. 8
C. 24
D. 120
E. 720
To count circular arrangements:
1. Place someone in the circle
2. Count the number of ways to arrange the REMAINING people

Once Alice has been placed in the circle:
Number of options for Bob = 1. (Must be in the seat opposite Alice)
Number of options for Cindy = 4. (Any of the 4 remaining seats)
Number of options for Darren = 1. (Must be in the seat opposite Cindy)
Number of options for Eddie =2. (Either of the 2 remaining seats)
Number of options for Fabian = 1. (The last remaining seat)
To combine these options, we multiply:
1*4*1*2*1 = 8

The correct answer is B.
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by Max@Math Revolution » Tue Mar 12, 2019 11:36 pm
=>

Note: Because the table is round, Alice's choice of chair does not change the number of possible arrangements.

Once Alice is seated, Bob's position is determined. Cindy has 4 remaining possible seats. Cindy's choice determines Darren's position. Eddie then has 2 remaining possible seats, and Fabian must sit in the remaining chair.
Thus, the number of possible arrangements is 4*2 = 8.

Therefore, B is the answer.
Answer: B
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