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Find the total number of permutations of...

Find the total number of permutations of `n` different things taken not more than `r` at a time, when each thing may be repeated any number of times.

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To find the total number of permutations of \( n \) different things taken not more than \( r \) at a time, when each thing may be repeated any number of times, we can follow these steps: ### Step-by-Step Solution: 1. **Understanding the Problem**: We have \( n \) different items and we want to find permutations of these items taken up to \( r \) at a time, allowing for repetition. 2. **Permutations for Each Position**: ...
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