Question

Three schools send $2,4$ and $6$ students, respectively, to a summer camp. The $12$ students must be accommodated in 6 rooms numbered $1,2,3,4,5,6$ in such a way that each room has exactly $2$ students and both from the same school. The number of ways, the students can be accommodated in the rooms is

• A. $60$
• B. $45$
• C. $32400$
• D. $2700$

Answer 1

The correct option is C $32400$

Dividing the $6$ students into $3$ groups of $2$
$=\frac{6!}{(2!{)}^3\times 3!}$
Dividing the $4$ students into $2$ groups of $2$
$=\frac{4!}{(2!{)}^2\times 2!}$

Number of possible ways
$=\frac{6!}{(2!{)}^3\times 3!}\times \frac{4!}{(2!{)}^2\times 2!}\times 6!=32400$