CAT 2017 Question Paper | Quants Slot 1

CAT Questions

TThe question is from Permutation and Combination. We need to find out the number of ways of distributing identical erasers among kids. This section hosts several 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 7 identical erasers be distributed among 4 kids in such a way that each kid gets at least one eraser but nobody gets more than 3 erasers ?

1. 16
2. 20
3. 14
4. 15

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Video Explanation

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Explanatory Answer

Method of solving this CAT Question from Permutation and Combination

Given that 7 identical erasers be distributed among 4 kids in such a way that each kid gets at least one eraser but nobody gets more than 3 erasers.
We have to find by how many number of ways the erasers are distributed such that each kid gets at least one eraser but no body gets more than 3 erasers.
Let us assume the 4 kids to be a , b , c , d such that a + b + c + d = 7.
It can be distributed in ⁶C₃ ways
⟹ \\frac{6 × 5 × 4}{3 × 2 × 1}) = 20
It is given that no body gets more than 3 erasers so let us say that one kid could get 4 , 5 , 6 eraser.
If one kid a, gets 4 erasers the other kids b , c , d can get each one respectively such that 4 , 1 , 1 , 1 or 1 , 1 , 1 , 4 or 1 , 4 , 1 , 1 or 1 , 1 , 4 , 1 so there are chances of 4 ways.
So, 20 – 4 = 16 ways

The question is "In how many ways can 7 identical erasers be distributed among 4 kids in such a way that each kid gets at least one eraser but nobody gets more than 3 erasers ?"

Hence, the answer is 16

Choice A is the correct answer