In how many ways can a team of $3$ boys and $3$ girls be selected from $5$ boys and $4$ girls?

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

Evaluate $\frac{n!}{r!(n-r)!}$ when $n=5$ and $r=2$.

$A$ student is to answer $10$ out of $13$ questions in an examination such that he must choose at least $4$ from the first $5$ questions. The number of choices available to him is

If ${ }^{(n-1)} C_3+{ }^{(n-1)} C_4>{ }^n C_3$,then the minimum value of $n$ is

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