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

In how many ways can five examination papers be arranged so that physics and chemistry papers never come together?

The total number of words that can be formed by using all the letters of the word $ALLEN$ such that all vowels occur in alphabetical order is:

How many numbers between $5000$ and $10,000$ can be formed using the digits $1, 2, 3, 4, 5, 6, 7, 8, 9$ if each digit appears not more than once in each number?

If $^nP_5 = 9 \times ^{n-1}P_4$,then the value of $n$ is

The Chief Ministers of $11$ States of India meet to discuss the language problem. In how many ways can they seat themselves at a round table so that the Punjab and Madras Chief Ministers sit together?