The number of all $5$-digit numbers with distinct digits is:

$A$ number lock consists of three rings. If the $1^{st}$ ring is marked with digits $0$ to $9$,the $2^{nd}$ ring is marked with prime numbers greater than $2$ but less than $30$,and the $3^{rd}$ ring is marked with all vowels,find the total number of unsuccessful attempts.

The number of ways in which $n$ boys and $n$ girls can be arranged in a row such that all the boys are together and all the girls are also together is equal to

If $^n{P_r} = 720 \times {^n{C_r}}$,then $r$ is equal to:

How many words can be formed using the letters of the word $SCHOLAR$ that start with $A$ and end with $S$?

All the letters of the word $EAMCET$ are arranged in all possible ways. The number of such arrangements in which two vowels are not adjacent to each other is