The number of all four-digit numbers that can be formed with the digits $0, 1, 2, 3, 4, 5$ when the repetition of the digits is not allowed,is

The number of words,which can be formed using all the letters of the word $\text{DAUGHTER}$,so that all the vowels never come together,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.

On the occasion of the Dipawali festival, each student of a class sends a greeting card to every other student. If there are $20$ students in the class, the total number of greeting cards sent by the students is:

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

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