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) First,arrange the $6$ men at a round table. The number of ways to arrange $n$ objects in a circle is $(n-1)!$. So,$6$ men can be arranged in $(6-1

Vedclass · Accepted Answer

$6! 	imes 5!$

Vedclass · Answer

(A) First,arrange the $6$ men at a round table. The number of ways to arrange $n$ objects in a circle is $(n-1)!$. So,$6$ men can be arranged in $(6-1)! = 5!$ ways.After arranging the men,there are $6$ gaps created between them.Since no two women should sit together,we need to place $5$ women in these $6$ gaps.The number of ways to choose $5$ gaps out of $6$ is $^6C_5$,and the $5$ women can be arranged in these gaps in $5!$ ways.Alternatively,we can place $5$ women in $6$ gaps in $P(6, 5)$ ways.Total number of ways $= 5! 	imes P(6, 5) = 5! 	imes \frac{6!}{(6-5)!} = 5! 	imes 6!$.

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

The number of circular permutations of $n$ distinct objects is......

The number of ways in which $8$ different pearls can be arranged to form a necklace is

$A$ person invites $8$ guests to a dinner and places $5$ of them at one table and the remaining $3$ at another,both the tables being round. The number of ways in which the guests can be arranged is

The number of circular permutations of $n$ different objects is

Find the number of ways in which two Americans,two British,one Chinese,one Dutch,and one Egyptian can sit at a round table so that persons of the same nationality are separated.

Vedclass Test Series

Exam Paper Generator

Online Exam Module