Three schools send 2, 4, and 6 students,respe | vedclass

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

Question

(C) The number of students from the three schools are $2, 4,$ and $6$. Since each room must contain $2$ students from the same school,we divide the st

Vedclass · Accepted Answer

$32400$

Vedclass · Answer

(C) The number of students from the three schools are $2, 4,$ and $6$. Since each room must contain $2$ students from the same school,we divide the students into groups of $2$: School $1$ has $1$ group of $2$ students. School $2$ has $2$ groups of $2$ students. School $3$ has $3$ groups of $2$ students. Total number of groups $= 1 + 2 + 3 = 6$ groups. First,we arrange these $6$ groups into the $6$ distinct rooms,which can be done in $6!$ ways. Next,we consider the internal arrangements of the students within the schools: For school $2$,the $4$ students are divided into $2$ groups of $2$. The number of ways to do this is $\frac{4!}{2! 	imes 2! 	imes 2!} = 3$. For school $3$,the $6$ students are divided into $3$ groups of $2$. The number of ways to do this is $\frac{6!}{2! 	imes 2! 	imes 2! 	imes 3!} = 15$. Total ways $= 6! 	imes 3 	imes 15 = 720 	imes 45 = 32400$.

Similar Questions

Five balls of different colors are to be placed in three boxes of different sizes,where each box can hold all five balls. In how many ways can the balls be placed such that no box remains empty?

Let $0 \leq r \leq n$. If ${ }^{n+1} C_{r+1} : { }^{n} C_{r} : { }^{n-1} C_{r-1} = 55 : 35 : 21$,then $2n + 5r$ is equal to:

The number of $4$ letter words (with or without meaning) that can be formed from the eleven letters of the word $'EXAMINATION'$ is

If the number of seven-digit numbers,such that the sum of their digits is even,is $m \cdot n \cdot 10^{n}$; $m, n \in \{1, 2, 3, \ldots, 9\}$,then $m+n$ is equal to . . . . . . .

$A$ string of letters is to be formed by using $4$ letters from all the letters of the word "$MATHEMATICS$". The number of ways this can be done such that two letters are of the same kind and the other two are of a different kind is:

Vedclass Test Series

Exam Paper Generator

Online Exam Module