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

In a conference of $8$ persons,if each person shakes hands with every other person exactly once,then the total number of handshakes is:

$A$ person goes in for an examination in which there are four papers with a maximum of $m$ marks from each paper. The number of ways in which one can get $2m$ marks is

There are $(n + 1)$ white and $(n + 1)$ black balls,each set numbered $1$ to $(n + 1)$. The number of ways in which the balls can be arranged in a row so that the adjacent balls are of different colours is

$A$ man has $7$ friends. In how many ways can he invite one or more of them for a tea party?

The number of words formed from the letters of the word $RAJASTHAN$ by taking all the letters at a time in which vowels are alternate is: