How many permutations can be made by using all the letters of the word $MATHEMAGICA$?

How many different ways can the letters in the word $ATTEND$ be arranged?

The number of ways in which $10$ persons can go in two boats so that there may be $5$ on each boat,supposing that two particular persons will not go in the same boat is:

$A$ man has $10$ friends. In how many ways can he invite one or more of them to a party?

$m$ men and $n$ women are to be seated in a row so that no two women sit together. If $m > n$,then the number of ways in which they can be seated is

$A$ 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