In a row,6 boys and 6 girls are arranged at r | vedclass

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

Question

(D) Total number of ways to arrange $12$ people ($6$ boys and $6$ girls) is $12!$.To find the number of ways where $6$ girls are together,we treat the

Vedclass · Accepted Answer

$1/132$

Vedclass · Answer

(D) Total number of ways to arrange $12$ people ($6$ boys and $6$ girls) is $12!$.To find the number of ways where $6$ girls are together,we treat the $6$ girls as a single unit. Now,we have $6$ boys and $1$ unit of girls,totaling $7$ entities.These $7$ entities can be arranged in $7!$ ways.The $6$ girls within their unit can be arranged in $6!$ ways.So,the number of favorable arrangements is $7! 	imes 6!$.The probability $P$ is given by $\frac{	ext{Favorable outcomes}}{	ext{Total outcomes}} = \frac{7! 	imes 6!}{12!}$.$P = \frac{7! 	imes 6 	imes 5 	imes 4 	imes 3 	imes 2 	imes 1}{12 	imes 11 	imes 10 	imes 9 	imes 8 	imes 7!} = \frac{720}{95040} = \frac{1}{132}$.

In a row,$6$ boys and $6$ girls are arranged at random. Find the probability that all $6$ girls are together.

Similar Questions

If the number of diagonals in a polygon with $n$ sides is $275$,then $n = .....$

The number of diagonals in a convex polygon with $n$ sides is .....

$15$ persons are sitting around a circular table. The number of ways of selecting three persons at a time from them,such that the selected three do not sit together at one place is

$m$ 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

How many parallelograms can be formed by a set of $4$ parallel lines intersecting another set of $3$ parallel lines?

Vedclass Test Series

Exam Paper Generator

Online Exam Module