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In how many of the permutations of n thi...

In how many of the permutations of `n` thing taken `r` at a time will three given things occur?

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To solve the problem of finding how many permutations of `n` things taken `r` at a time will include three specific items, we can follow these steps: ### Step-by-Step Solution: 1. **Identify the Fixed Items**: We know that three specific items must be included in every permutation. Let's denote these three items as A, B, and C. 2. **Adjust the Total Count**: Since we are including A, B, and C in every permutation, we need to adjust the total number of items. Thus, the number of remaining items will be \( n - 3 \) (since we are excluding A, B, and C). ...
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