If a person has $3$ coins of different denominations,the number of different sums that can be formed is

$A$ student has to answer $10$ questions,choosing at least $4$ from each of the parts $A$ and $B$. If there are $6$ questions in part $A$ and $7$ in part $B$,then the number of ways the student can choose $10$ questions is:

The number of ordered triplets of positive integers which are solutions of the equation $x + y + z = 100$ is

What is the total number of ways of choosing $4$ cards from a pack of $52$ playing cards? In how many of these are the $4$ cards of the same colour?

$A$ student is asked to answer $10$ out of $13$ questions in an examination such that he must answer at least four questions from the first five questions. Then the total number of possible choices available to him is

The number of ways in which $21$ identical apples can be distributed among three children such that each child gets at least $2$ apples,is