There are 10 professors and 20 students out of whom a committee of 2 professors and 3 students is to be formed. Find the number of ways in which this can be done. Further find in how many of these committees:
A particular professor is included
A particular student is included
A Particular student is excluded

Explanation

To solve the problem, we need to break it down into parts. We have 10 professors and 20 students, and we need to form a committee consisting of 2 professors and 3 students.

### Step 1: Calculate the total number of ways to form the committee

1. **Choosing 2 professors from 10**:
The number of ways to choose 2 professors from 10 is given by the combination formula:
\[
\binom{n}{r} = \frac{n!}{r!(n-r)!}
...