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:

There are $10$ persons named $A, B, \dots, J$. We have the capacity to accommodate only $5$. In how many ways can we arrange them in a line if $A$ must be included and $G$ and $H$ must not be included in the team of $5$?

The total number of different combinations of one or more letters which can be made from the letters of the word '$MISSISSIPPI$' is

In how many ways can $5$ sportsmen be selected from a group of $10$?

In the given figure,$6$ '$A$'s should be written in such a manner that every row contains at least one '$A$'. The number of ways this is possible is: