The number of ways in which 6 men and 5 women | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(A) To arrange $6$ men and $5$ women at a round table such that no two women sit together,we use the gap method.First,arrange the $6$ men at the round

Vedclass · Accepted Answer

$6! 	imes 5!$

Vedclass · Answer

(A) To arrange $6$ men and $5$ women at a round table such that no two women sit together,we use the gap method.First,arrange the $6$ men at the round table. The number of ways to arrange $n$ distinct objects in a circle is $(n-1)!$.So,the number of ways to arrange $6$ men is $(6-1)! = 5!$.This arrangement creates $6$ gaps between the men (including the gap between the last and first man).Since there are $5$ women and they must not sit together,we need to place them in these $6$ available gaps.The number of ways to choose $5$ gaps out of $6$ is $^6C_5$,and the number of ways to arrange the $5$ women in these gaps is $5!$.Thus,the total number of ways is $5! 	imes ^6C_5 	imes 5! = 5! 	imes 6 	imes 5! = 6! 	imes 5!$.

The number of ways in which $6$ men and $5$ women can dine at a round table if no two women are to sit together is given by

Similar Questions

There are $n$ white and $n$ black balls marked $1, 2, 3, ..., n$. The number of ways in which we can arrange these balls in a row so that neighbouring balls are of different colours are

The number of diagonals in a polygon of $m$ sides is

If $n$ is a factor of $72$,such that $xy = n$,then the number of ordered pairs $(x, y)$ is: (where $x, y \in N$)

$^{47}C_4 + \sum_{r=1}^{5} {}^{52-r}C_3 = $

In how many different ways can the letters of the word '$KURUKSHETRA$' be arranged?

Vedclass Test Series

Exam Paper Generator

Online Exam Module