Question:
In how many ways can eight directors, the vice chairman and chairman of a firm be seated at a round table, if the chairman has to sit between the vice chairman and a specific director?
In how many ways can eight directors, the vice chairman and chairman of a firm be seated at a round table, if the chairman has to sit between the vice chairman and a specific director?
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Treat the chairman with his two neighbours (the vice chairman and the specific director) as one block and count circular arrangements.
Updated On: Nov 4, 2026
- \(9! \times 2\)
- \(2 \times 7!\)
- \(2 \times 8!\)
- None of these
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The Correct Option is B
Solution and Explanation
Step 1: Count the people:
There are 8 directors + 1 vice chairman + 1 chairman = 10 people.
Step 2: Make a block:
The chairman sits between the vice chairman and the specific director, so the block is (VC, Chairman, Director) or (Director, Chairman, VC). The block can be arranged internally in 2 ways.
Step 3: Arrange around the table:
The block plus the other 7 directors make 8 units. Arranging 8 units in a circle gives \((8-1)! = 7!\) ways.
Step 4: Multiply:
Total = \(2 \times 7!\) = 10080.
Final Answer:
The correct option is (2): \(2 \times 7!\)
There are 8 directors + 1 vice chairman + 1 chairman = 10 people.
Step 2: Make a block:
The chairman sits between the vice chairman and the specific director, so the block is (VC, Chairman, Director) or (Director, Chairman, VC). The block can be arranged internally in 2 ways.
Step 3: Arrange around the table:
The block plus the other 7 directors make 8 units. Arranging 8 units in a circle gives \((8-1)! = 7!\) ways.
Step 4: Multiply:
Total = \(2 \times 7!\) = 10080.
Final Answer:
The correct option is (2): \(2 \times 7!\)
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