Question

12 persons are to be arranged to a round table. If two particular persons among them are not to be side by side, the total number of arrangements is:

Answer 1

Answer:

9 x 10! ways = 32659200 ways

Step-by-step explanation:

Let us assume that A and B are not to be side by side.

Let’s start the arrangement with A.

1) A can sit in on any chair. This can be done in 1 way since it is a circle. If only it were a row, A can sit in 12 ways. Since it is a circle, we cannot decide the count. So we simply put A in the spot.

2) Now, B cannot sit in the seat that we place A in. B cannot even sit in the 2 seats left and right to A. So, B can sit in 9 seats.

3) Now the remains 10 can sit in 10! Ways.

Therefore, the number of ways the required arrangement can be done = 9 x 10! ways = 32659200 ways