# Then number of ways of distributing 8 identical balls in 3 distinct boxes so that none of the boxes is empty is Option 1) Option 2) 21 Option 3) 5 Option 4)

As we learnt in

Theorem of Number of Solutions -

Number of non-negative integral solutions of the equation x1 + x2 + x3 +......... + xr=n is .

- wherein

Where

Let the number of balls in 3 boxes be x, y, z.

x + y + z = 8

(x - 1) + (y - 1) + (z - 1) = 8 - 3

x' + y' + z' = 5

Positive integral solutions are

Correct option is 2.

Option 1)

This is an incorrect option.

Option 2)

21

This is the correct option.

Option 3)

5

This is an incorrect option.

Option 4)

This is an incorrect option.

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