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?
Question
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?
Solution
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!].
Similar Questions
In a restaurant, 19 men and 9 women are seated on 28 chairs at a round table. Find the total number of possible ways such that 19 men are always sitting next to each other.10! x 19!9! x 19!8! x 18!27!
1 pointIn a restaurant, 10 men and 6 women are seated on 16 chairs at a round table. Find the total number of possible ways such that 10 men are always sitting next to each other.
If m men and n women are to be seated in a row so that no two women sit together. If m>n, then the number of ways in which they can be seated is
Question:-Nine chairs are numbered 1 to 9. Three women and four men wish to occupy one chair each. First the women chose the chairs from amongst the chair marked 1 to 5; and then the men select the chairs from amongst the remaining. The number of possible arrangements isChoices:- 5C3 × 4C2 5C2 × 4P3 5C3 × 6C4 None of these
Each of two women and three men is to occupy one chair out of eight chairs, each of which is numbered from one to eight. First , women are to occupy any two chairs from those numbered one to four, and then the three men would occupy any three chairs out of the remaining six chairs. What is the maximum number of different ways in which this can be done ?Options4014403660132
Upgrade your grade with Knowee
Get personalized homework help. Review tough concepts in more detail, or go deeper into your topic by exploring other relevant questions.