CAT 2017 Slot 1 — QA 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?
Answer & solution
16
- B
20
- C
14
- D
15
After giving one eraser to each of the 4 kids, there are 3 left.
They can split 2, 1 or 1, 1, 1. (No kid can get 4)
Number of ways of 2, 1 split = 4P2
Number of ways of 1, 1, 1 split = 4C3
There are 4P2 + 4C3, i.e., 16 ways of distributing the erasers.
Alternately,
Let the number of erasers given to the 4 kids be w, x, y, z.
w + x + y + z = 7.
After giving at least 1 eraser to each, 3 erasers will be left.
w' + x' + y' + z' = 3
The number of positive integral solutions is 3 + 4 - 1C4 - 1, i.e. 20. This includes (4,1,1,1); (1,4,1,1); (1,1,4,1); (1,1,1,4).
The required number = 20 – 4 = 16.
Hence, option (a).