The question is from Permutation and Combination. This question is about Selection. Our task is find out the number ways of allotting room under given condition. This section hosts a number of questions which are on par with CAT questions in difficulty on CAT Permutation and Combination, and CAT Probability.

Question 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?

- 6 * 5 ! ways
- 7 * 5 ! ways
- 3 * 3 ! ways
- 15 * 5 ! ways

15 * 5 ! ways

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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.

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

Choice D is the correct answer.

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