The number of arrangements of the letters of the word $CALCUTTA$ is:

In how many ways can $n$ books be arranged in a row so that two specified books are not together?

From $6$ different novels and $3$ different dictionaries,$4$ novels and $1$ dictionary are to be selected and arranged in a row on a shelf so that the dictionary is always in the middle. The number of such arrangements is :

There are $6$ men and $8$ women in a club in which a committee of $5$ people has to be formed. What will be the number of ways to select $5$ people if no man is selected?

Let $T_n$ denote the number of triangles which can be formed using the vertices of a regular polygon of $n$ sides. If $T_{n + 1} - T_n = 21$,then $n$ equals:

The number of ways in which the letters of the word $ARRANGE$ can be arranged such that both $R$ do not come together is