How many numbers of five digits can be formed with the digits $0, 1, 2, 3, 5$ and $6$?

On the occasion of the Deepawali festival,each student of a class sends greeting cards to all the others. If there are $20$ students in the class,then the total number of greeting cards exchanged by the students is:

The number of ways in which one or more balls can be selected out of $10$ white,$9$ green,and $7$ blue balls are:

$A$ student is to answer $10$ out of $13$ questions in an examination such that he must choose at least $4$ from the first $5$ questions. The number of choices available to him is

The number of ways in which $3$ boys and $4$ girls can be seated around a circular table if no two boys sit together is:

How many $3$-digit numbers can be formed by using the digits $0, 2, 3, 6, 8$ when the digits may be repeated any number of times?