Find the value of `r,` if
(i) `.^(11)P_(r)=990`
(ii) `.^(8)P_(5)+5*.^(8)P_(4)=.^(9)P_(r)`

Explanation

To solve the given problem, we will break it down into two parts as specified in the question.

### Part (i): Find the value of `r` if \( ^{11}P_r = 990 \)

1. **Understanding the Permutation Formula**:
The formula for permutations is given by:
\[
^nP_r = \frac{n!}{(n-r)!}
...