A committee of m members is to be chosen from a population of n students. What is your probability of being chosen?

A committee of $m$ students is being formed by randomly selecting from a population of n undergraduate students in an engineering college (note: m < n). Assume that you are also included in this population of students. What is the probability that you will be among the $m$ selected students?

Since you’re choosing $m$ amount of students to be in a committee from a population $n$, then the probability of any student being in the committee is $left(frac{m}n right)$. But the probability of you being chosen is $left(frac{1}m right)$. Since the students being selected are not replaced, I used the following equation:

$$
frac{left(frac{1}m right) left(frac{m-1}n right)}{left(frac{m}n right)}
$$

I feel like I am misunderstanding how permutations are used in this situation, so any insights on how to solve this question would be appreciated.