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Find the number of selections of one or ...

Find the number of selections of one or more things from the group of p identical things of one type, q identical things of another type, r identical things of the third type and n different things.

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To solve the problem of finding the number of selections of one or more things from a group of \( p \) identical things of one type, \( q \) identical things of another type, \( r \) identical things of a third type, and \( n \) different things, we can follow these steps: ### Step-by-Step Solution: 1. **Identifying Selections for Identical Things**: - For \( p \) identical things, the number of ways to select zero or more items is \( p + 1 \). This includes selecting none, one, two, ..., up to \( p \) items. - Similarly, for \( q \) identical things, the number of ways is \( q + 1 \). - For \( r \) identical things, the number of ways is \( r + 1 \). ...
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