How many $5$-digit numbers can be formed using the digits $0, 1, 2, 3, 5, 7$ without repetition? If all such numbers are arranged in ascending order,what is the rank of the number $70513$?

Ten persons,amongst whom are $A, B$ and $C$,are to speak at a function. The number of ways in which it can be done if $A$ wants to speak before $B$ and $B$ wants to speak before $C$ is:

How many numbers between $999$ and $10,000$ can be formed using the digits $0, 2, 3, 6, 7, 8$ without repetition?

How many $8$-digit numbers can be formed such that all digits are distinct?

We are to form different words with the letters of the word $INTEGER$. Let $m_1$ be the number of words in which $I$ and $N$ are never together and $m_2$ be the number of words which begin with $I$ and end with $R$,then $m_1/m_2$ is equal to

How many words,with or without meaning,can be formed using all the letters of the word $EQUATION$,using each letter exactly once?