Question

In how many ways can 6 boys be allotted into 5 rooms such that no room is empty and all 6 boys are accommodated

Answer 1

According to the question we have to arrange 6 boys in 5 rooms such that no room is empty and all the six boys are accommodated.

Out of the five rooms 4 room may have one boy each and the remaining one room will have two boys.

Now we can select the two boy from total of 6 in 6C2 fashion i.e. 15 ways.

Now this two boys again can be arranged in the 5 rooms in 5 ways.

Therefore 6 boys be allotted into 5 rooms such that no room is empty and all 6 boys are accommodated in 15 * 5 ! ways

Answer 2

Answer: 15 * 5 ! ways

Step-by-step explanation:

We can distribute boys in 2-1-1-1 fashion , that is we can put two boys in one room and the other rooms will have one boy each.We can pick two boys out of the 6 in 6C2 ways.And these two boys can be alloted to any one of the rooms in 5 ways. The remaining rooms can be filled in 4*3*2*1 ways.

SO, Totally the number of ways is 6C2*5! ways.

Correct Answer : 15 * 5 ! ways