How many words can be formed using the letters of the word $COURTESY$ such that the first letter is $C$ and the last letter is $Y$?

By using the non-zero digits,the number of $5$ digit numbers that can be formed such that each number has the largest digit in its middle place and the digits in the number are distinct is:

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

$5$-digit numbers are to be formed using $2, 3, 5, 7, 9$ without repeating the digits. If $p$ is the number of such numbers that exceed $20000$ and $q$ is the number of those that lie between $30000$ and $90000$,then $p : q$ is

What is the number of permutations of three letters $A, B, C$ taken all at a time?

The number of ways in which ten candidates $A_1, A_2, \dots, A_{10}$ can be ranked such that $A_1$ is always above $A_{10}$ is: