Permutations and Combinations

Let $r, l$ be two integers such that $r \geq l \geq 3$. What is the total number of functions$f : \{1, 2, \ldots, r\} \rightarrow \{1, 2, \ldots, r\}$such that $f(1), f(2), \ldots, f(l)$ are all distinct?

How many three digit numbers divisible by 5 are there in which no digits are repeated?

\(\text { What is the total number of distinct divisors of } 2^9 \times 3^{19} \text { ? }\)