Question

11 players of the Indian cricket team are sitting at a circular table. The number of ways they can sit so that two players, the wicket keeper and the captain never sit together is ___

• A. \(10!\)
• B. \(2\times 9!\)
• C. \(8\times 9!\)
• D. \(9\times 9!\)

Hint:

Count all circular arrangements, then subtract those where the two players sit together.

Answer 1

The Correct Option is C

Step 1: Fix one player:
Seat the captain first. Relative to him the keeper can sit in $10$ other seats, but $2$ of them are adjacent to the captain, so $8$ seats are allowed.

Step 2: Seat the rest:
The other $9$ players fill the remaining $9$ seats in $9!$ ways.
Total $= 8 \times 9!$.

Final Answer:
The count is $8 \times 9!$, option (C). \[ \boxed{8 \times 9!} \]