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Explanation:

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).

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