How many lines can be drawn through $21$ points on a circle?

The number of ways of selecting $15$ teams from $15$ men and $15$ women,such that each team consists of a man and a woman,is

In how many ways can $6$ persons stand in a queue at a time?

There are $6$ multiple choice questions in an examination. How many sequences of answers are possible,if the first three questions have $4$ choices each and the next three have $5$ choices each?

There are $6$ items in column $A$ and $6$ items in column $B$. $A$ student is asked to match each item in column $A$ with an item in column $B$. How many possible (correct or incorrect) answers are there to this question?

$A$ group of students comprises $5$ boys and $n$ girls. If the number of ways in which a team of $3$ students can be selected from this group such that there is at least one boy and at least one girl in each team is $1750$,then $n$ is equal to: