Out of $10$ white,$9$ black and $7$ red balls,the number of ways in which selection of one or more balls can be made,is

The product of any $r$ consecutive natural numbers is always divisible by

$A$ 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:

There are $5$ types of ice creams available in a shop. $A$ child buys $6$ ice creams.
Statement-$1$: The child can buy $6$ ice creams in $^{10}C_5$ ways.
Statement-$2$: The number of ways the child can buy $6$ ice creams is equal to the number of ways to arrange $6$ '$A$'s and $4$ '$B$'s in a row.

The number of solutions of the equation $x+y+z=10$, where $x, y$, and $z$ are positive integers, is:

In how many ways can a committee consisting of one or more members be formed out of $12$ members of the Municipal Corporation?