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How many ways can be distributed to the box of (n+1) didferents balls provided that "bo...

How many ways can be distributed to the box of (n+1) didferents balls provided that "bo box remains empty".

Math   Statistics-And-Probability   
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Answer #1

Let's consider boxes to be "r" and the number of balls needs to be distributed is n

The Formula to calculate the number of ways is written in the Image.

In the given formula, substitute, n as n+1 different balls a mentioned in the question.

Derivation Approach

It's related to the concept of Inclusion - Exclusions of ways

Inclusion-Exclusion Formula is given in the image above.

Thank You!

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