If ` ""^(22)P_(r+1):""^(20)P_(r+2)=11:52,` find r.

Explanation

To solve the problem \( \frac{^{22}P_{r+1}}{^{20}P_{r+2}} = \frac{11}{52} \), we will start by expressing the permutations in terms of factorials.

### Step 1: Write the permutations in factorial form
The permutation \( ^nP_r \) is defined as \( \frac{n!}{(n-r)!} \). Therefore, we can write:

\[ ^{22}P_{r+1} = \frac{22!}{(22 - (r + 1))!} = \frac{22!}{(21 - r)!} \]
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