(i) If `""^(15)P_(r)=2730,` find the value of r.
(ii) If ` ""^(10)P_(r)=5040,` find the value of r.

Explanation

To solve the given problems, we will use the formula for permutations, which is defined as:

\[ _nP_r = \frac{n!}{(n-r)!} \]

### Part (i): Given \( 15P_r = 2730 \)

...