CAT Quantitative Aptitude Questions | CAT Permutation and Combination Questions

The question is from Permutation and Combination. Another question on counting. We need to find out the number of ways of placing toys in boxes. 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 3: In how many ways 11 identical toys be placed in 3 distinct boxes such that no box is empty?

1. 72
2. 54
3. 45
4. 36

Explanatory Answer

Method of solving this CAT Question from Permutation and Combination: Another wonderful question. A classic question that is from a standard template once a layer is removed.

This is nothing but the number of ways of having a, b, c such that a + b + c = 11, where a, b, c are natural numbers. By having them to be natural numbers, we ensure that no box can be empty. (no zeroes)

The question is similar to the previous one. ¹⁰C₂ = 45 ways

The question is "In how many ways 11 identical toys be placed in 3 distinct boxes such that no box is empty?"

Hence the answer is "45"

Choice C is the correct answer.