Question 21

In how many ways can 7 different balls be distributed in 5 different boxes. If any box can contain any number of balls except that ball 3 can only be put into box 3 or box 4 ?

Let's number the balls as 1, 2, 3, 4, 5, 6, 7.

We have a condition on ball 3; it can be placed in either box 3 or 4. So, ball 3 has two chances.

All the remaining balls can be placed in any of the five boxes. This can be done in 5*5*5*5*5*5=$$5^6$$

The total number of ways is $$2*5^6$$.

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