The number of ways in which $6$ distinct things can be distributed into $2$ boxes so that no box is empty 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

$A$ company has $10$ employees. The company has decided to form a team including at least three employees and also excluding at least three employees. Then the number of ways of forming the team is

In how many ways can $35$ apples be distributed among $3$ boys such that each boy can have any number of apples?

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

$A$ student has to answer $10$ out of $13$ questions in an examination. The number of ways in which he can answer if he must answer at least $3$ of the first $5$ questions is: