CAT Quantitative Aptitude Questions | CAT Permutation and Combination Questions

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?

1. 6 * 5 ! ways
2. 7 * 5 ! ways
3. 3 * 3 ! ways
4. 15 * 5 ! ways

Explanatory Answer

Method of solving this CAT Question from Permutation and Combination: Normal Selection applies for the extra person!!

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.

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?"

Hence the answer is "15 * 5 ! ways "

Choice D is the correct answer.