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:

In how many ways can a student choose a programme of $5$ courses if $9$ courses are available and $2$ courses are compulsory for every student?

There are $6$ members to be selected for a group to be sent abroad from a total of $12$ members. In how many ways can the selection be made such that a particular member is always excluded?

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

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

Suppose that $20$ pillars of the same height have been erected along the boundary of a circular stadium. If the top of each pillar is connected by beams to the top of all its non-adjacent pillars,then the total number of beams is: