In how many ways can 5 boys be allotted four different sofas such that none of the sofas are empty and all the 5 boys are accommodated? Choices
A) 300
B) 290
C) 280
D) 260
E) 240
4 boys can be selected from 5 boys in 5C4 ways = 5   4 boys can be arranged in 4 rooms in 4! ways   and since 1 boy has to share a room with one of the 4 boys, therefore total ways = 2! = 2   Hence total number of ways in which allocation can be done = 5C4 * 4! * 2! = 5*2*4! =240   240
<result>E</result>
In how many ways can 5 boys be allotted four different sofas such that none of the sofas are empty and all the 5 boys are accommodated?