There are $10$ points in a row. In how many ways can $4$ points be selected such that no two of them are consecutive?

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 numbers of four digits can be formed with the digits $1, 2, 3, 4$ and $5$?

How many words comprising of any three letters of the word $UNIVERSAL$ can be formed?

All the five-digit numbers in which each successive digit exceeds its predecessor are arranged in the increasing order of their magnitude. The $97^{th}$ number in the list does not contain the digit:

$A$ student is to answer $10$ out of $13$ questions in an examination such that he must choose at least $4$ from the first $5$ questions. The number of choices available to him is