The number of non-negative integral solutions of $x_1+x_2+x_3+x_4=10$ is

There are $4$ oranges,$5$ apples,and $7$ mangoes in a fruit basket. The number of ways of selecting at least one fruit from among the fruits in the basket 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:

$A$ bag contains $3$ coins of one rupee,$4$ coins of fifty paise,and $5$ coins of ten paise. If at least one coin is selected from the bag,what is the total number of ways to make the selection?

If ${ }^{n+4} C_{n+1}-{ }^{n+3} C_n=15(n+2)$,then $n=$

If $5$ dice are rolled simultaneously,then the number of ways of getting a total of $7$ on their faces is: