If 3 sisters and 8 brothers are together play | vedclass

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

Question

(D) Total number of people = $3 + 8 = 11$. Number of ways to arrange $11$ people around a circle = $(11 - 1)! = 10!$. Now,consider the case where all

Vedclass · Accepted Answer

$8! 	imes 84$

Vedclass · Answer

(D) Total number of people = $3 + 8 = 11$. Number of ways to arrange $11$ people around a circle = $(11 - 1)! = 10!$. Now,consider the case where all $3$ sisters sit together. Treat the $3$ sisters as $1$ unit. Total units to arrange = $8$ brothers + $1$ unit of sisters = $9$ units. Number of ways to arrange $9$ units around a circle = $(9 - 1)! = 8!$. The $3$ sisters can be arranged among themselves in $3! = 6$ ways. So,the number of ways where all $3$ sisters sit together = $8! 	imes 6$. The number of ways where all $3$ sisters are not seated together = (Total arrangements) - (Arrangements where all $3$ sisters sit together) = $10! - (8! 	imes 6)$. $10! - 6 	imes 8! = (10 	imes 9 	imes 8!) - (6 	imes 8!) = (90 - 6) 	imes 8! = 84 	imes 8!$.

If $3$ sisters and $8$ brothers are together playing a game,then the number of ways in which all the sisters and brothers are to be seated around a circle such that all the $3$ sisters are not seated together is

Similar Questions

The number of different ways of preparing a garland by using $6$ distinct white roses and $6$ distinct red roses such that no two red roses come together is

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

The number of ways that $8$ beads of different colours can be strung as a necklace is

In how many ways can $8$ beads of different colors be strung into a necklace?

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

Vedclass Test Series

Exam Paper Generator

Online Exam Module