The number of ways in which $17$ apples can be distributed among $4$ guests such that each guest gets at least $3$ apples is

Consider a class of $5$ girls and $7$ boys. The number of different teams consisting of $2$ girls and $3$ boys that can be formed from this class,if there are two specific boys $A$ and $B$ who refuse to be members of the same team,is

Given $5$ different green toys,$4$ different blue toys,and $3$ different red toys,how many combinations of toys can be chosen taking at least one green and one blue toy?

If ${}^{n-1}C_3 + {}^{n-1}C_4 > {}^{n}C_3$,then $n$ is just greater than which integer?

$A$ die is rolled three times. Find the probability of getting a larger number than the previous number each time.

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