The number of circular permutations of $n$ different objects is

The number of $7$-digit numbers which can be formed using the digits $1, 2, 3, 2, 3, 3, 4$ is:

How many words can be formed using the letters of the word $INDEPENDENCE$,such that all vowels always come together?

The number of ways in which $3$ children can distribute $10$ tickets out of $15$ consecutively numbered tickets among themselves such that they get consecutive blocks of $5, 3$ and $2$ tickets is:

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

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: