In how many ways can $mn$ letters be posted in $n$ letter-boxes?

How many numbers lying between $999$ and $10000$ can be formed with the help of the digits $0, 2, 3, 6, 7, 8$ when the digits are not to be repeated?

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

In how many different ways can the letters of the word '$AUCTION$' be arranged in such a way that the vowels always come together?

$A$ committee of $5$ members is to be formed out of $3$ trainees,$4$ professors,and $6$ research associates. In how many different ways can this be done if the committee must have $2$ trainees and $3$ research associates?

Six married couples decide to form a committee of $6$ persons. The total number of ways to form the committee such that it contains no couples is equal to: