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 ^{6}C_{2} 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 ^{6}C_{2}*5! ways.
Correct Answer : 15 * 5 ! ways