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

Explanation

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

### Step 1: Write the permutation formulas
The permutation formula is given by:
\[ nP_r = \frac{n!}{(n-r)!} \]
Thus, we can express \( 22P_{r+1} \) and \( 20P_{r+2} \) as follows:
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