Distributing Identical Erasers

CAT 2017 Slot 1 · QA · Hard · Permutation and Combination

All CAT 2017 Slot 1 questionsMore Permutation and Combination questionsAll CAT QA

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. A.

    16

  2. B.

    20

  3. C.

    14

  4. D.

    15

Answer

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: 4×3=124 \times 3 = 12 ways.
  • 1 to three kids: (43)=4\binom{4}{3} = 4 ways. Total ways = 12+4=1612 + 4 = 16.

Practise this under exam conditions

Sign in to solve it with a live timer, the on-screen CAT calculator, and streak and accuracy tracking across every question you attempt.

Solve in the workspace