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

There are $12$ members in a group. In how many ways can a team of $6$ members be selected such that a particular member is always included?

The number of $4$-digit numbers that can be formed from the digits $0, 1, 2, 3, 4, 5, 6, 7$ such that each number contains the digit $1$ is:

$A$ number lock on a suitcase has $3$ wheels,each labelled with $10$ digits from $0$ to $9$. If opening the lock requires a particular sequence of $3$ digits with no repeats,how many such sequences are possible?

In how many different ways can the letters of the word $MATHEMATICS$ be arranged?

There are $6$ men and $8$ women in a club,and a committee of $5$ people must be formed. What will be the number of ways to select $5$ people if only men are selected?