Distributing Identical Erasers
CAT 2017 Slot 1 · Quantitative Ability · Hard · Permutation and Combination
This is a hard Quantitative Ability question from the CAT 2017 Slot 1 paper. It tests Permutation and Combination. The full answer key and a step-by-step explanation are below — try it yourself first, then reveal the solution.
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?
- A.
16
- B.
20
- C.
14
- D.
15
A
Explanation
Give 1 eraser to each kid first. 3 erasers remain to be distributed among 4 kids. No kid can get more than 2 extra erasers (since max is 3 erasers per kid). Ways to distribute 3 extra erasers among 4 kids:
- All 3 to one kid: not allowed (since max extra = 2).
- 2 to one kid, 1 to another: ways.
- 1 to three kids: ways. Total ways = .
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