In how many ways can $6$ apples be distributed among $3$ boys,there being no restriction to the number of apples each boy may get?

Four-digit numbers are formed using the digits $1, 2, 3, 4$ (repetition is allowed). The number of such four-digit numbers divisible by $11$ is

How many numbers between $5000$ and $10,000$ can be formed using the digits $1, 2, 3, 4, 5, 6, 7, 8, 9$ if each digit appears not more than once in each number?

Let $A = \{a_1, a_2, a_3, ..., a_n\}$ be a set containing $n$ elements. Two subsets $P$ and $Q$ of $A$ are formed independently. The number of ways in which these subsets can be formed such that $(P - Q)$ contains exactly $2$ elements is:

The number of four-letter words that can be formed from the letters of the word '$MAYANK$' such that both '$A$'s are included but never together is equal to:

There are $3$ different rings to be worn in four fingers with at most $1$ in each finger. In how many ways can this be done?