There are 14 men and 9 women. They are to be seated on 23 chairsin a row such that no two women sit next to each other. How manyways are possible?

To solve this problem, we can use the concept of permutations and combinations.

Step 1: Arrange the 14 men first. They can be arranged in 14! ways.

Step 2: Now, we have 15 spaces (14 between the men and 1 on each end) where we can place the 9 women such that no two women are next to each other.

Step 3: We can select 9 spaces out of 15 to place the women. This can be done in 15C9 ways.

Step 4: The women can be arranged among themselves in 9! ways.

So, the total number of ways the men and women can be seated is 14! * 15C9 * 9!.

Note: 14! means factorial of 14 which is the product of all positive integers up to 14. Similarly, 15C9 is the number of ways to choose 9 items from 15, which is calculated as 15! / [(15-9)! * 9!].