Questionbank: Permutation and Probability

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Normal Selection applies for the extra person!!

Room Allocation

    Q.32: In how many ways can 6 boys be allotted into 5 rooms such that no room is empty and all 6 boys are accommodated?
    1. 6 * 5 ! ways
    2. 7 * 5 ! ways
    3. 3 * 3 ! ways
    4. 15 * 5 ! ways


  • Correct Answer
    Choice D. 15 * 5 ! ways

Detailed Solution

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

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