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?

In how many ways can $5$ prizes be distributed among four students when every student can take one or more prizes?

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?

There are four balls of different colours and four boxes of colours same as those of the balls. The number of ways in which the balls,one in each box,could be placed such that a ball does not go to the box of its own colour is

The number of ways in which $5$ boys and $3$ girls can be seated on a round table if a particular boy $B_1$ and a particular girl $G_1$ never sit adjacent to each other,is

How many $3$-digit numbers can be formed from the digits $2, 3, 5, 6, 7,$ and $9$ which are divisible by $5$,given that no digit is repeated?