The number of different words that can be formed from the letters of the word $SUCCESS$ in which the two $C$ are together but no two $S$ are together are:

There are $5$ roads leading to a town from a village. The number of different ways in which a villager can go to the town and return back is:

There are $m$ men and two women participating in a chess tournament. Each participant plays two games with every other participant. If the number of games played by the men between themselves exceeds the number of games played between the men and the women by $84,$ then the value of $m$ is

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

The number of $5$ digit telephone numbers having at least one of their digits repeated is

An eight-digit number divisible by $9$ is to be formed using digits from $0$ to $9$ without repeating the digits. The number of ways in which this can be done is: (in $(7!)$)