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

Three letters are chosen at random from the letters of the word $VARIABLE$ and all possible three-letter words (with or without meaning) are formed with them. Then the probability of getting a three-letter word having a consonant as its middle letter is

$^n{P_r} \div ^n{C_r} = $

The value of ${}^{47}C_4 + \sum_{j=1}^5 {}^{(52-j)}C_3$ is

The number of times the digit $5$ will be written when listing the integers from $1$ to $1000$ is

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