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

Explanation

To solve the problem \( \frac{22P_{r+1}}{20P_{r+2}} = \frac{11}{52} \), we will follow these steps:

### Step 1: Write the permutations in terms of factorials
Using the formula for permutations \( nP_r = \frac{n!}{(n-r)!} \), we can express \( 22P_{r+1} \) and \( 20P_{r+2} \):
\[ 22P_{r+1} = \frac{22!}{(22 - (r + 1))!} = \frac{22!}{(21 - r)!} \]
\[
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