How many different products can be obtained by multiplying two or more of the numbers $3, 5, 7, 11$ without repetition?

Find the number of ways in which a committee of $2$ teachers and $3$ students can be formed out of $10$ teachers and $20$ students. In how many of these committees a particular teacher is included?

Find the number of ways in which a committee of $2$ teachers and $3$ students can be formed out of $10$ teachers and $20$ students. In how many of these committees

a particular student is included?

Find the number of ways in which a committee of $2$ teachers and $3$ students can be formed out of $10$ teachers and $20$ students. In how many of these committees

a particular student is excluded?