In an examination,a student has to write exams in $8$ different subjects. He is declared fail if he fails in at least one subject. The number of ways in which he can fail is

$A$ debate club consists of $6$ girls and $4$ boys. $A$ team of $4$ members is to be selected from this club,including the selection of a captain (from among these $4$ members) for the team. If the team has to include at most one boy,then the number of ways of selecting the team is

The number of ways of giving $20$ distinct oranges to $3$ children such that each child gets at least one orange is $............$.

Assuming that the balls of the same color are identical,find the number of ways to select one or more balls from $10$ white,$9$ green,and $7$ black balls.

The number of ordered pairs $(x, y)$ of integers such that their product $xy$ is a positive integer less than $100$ is:

The number of four-letter words that can be formed using the letters of the word $BARRACK$ is