Question

Three schools send $2,4$ and $6$ students, respectively, to a summer camp. The $12$ students must be accommodation 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

Answer: (C)

$32400$

Ways of dividing students into groups of two from

i) 1st school $=\frac{2!}{2!}=1$

ii) 2nd school $=\frac{4!}{{(2!)}^2\times 2!}=3$

iii) 3rd school $=\frac{6!}{{(2!)}^3\times 3!}=15$

Total ways of dividing students $=1\times 3\times 15=45$

Total ways of arranging these groups in rooms $=45\times 6!=32400$