In an examination,there are $3$ multiple-choice questions,and each question has $4$ choices. The number of ways in which a student can fail to get all answers correct is:

$A$ question paper contains $4$ questions,each having $4$ alternative answers. The number of ways that a candidate can answer one or more questions is

The word $UNIVERSITY$ is arranged randomly. The probability that both $I$s do not come together is:

The number of four-digit numbers that can be formed using the digits $1, 2, 3, 4,$ and $5$ such that at least two digits are identical is

If $x$ and $y$ are digits such that $17! = 355687428096000$, then $x+y$ equals

$A$ bag contains $n$ white and $n$ black balls. Pairs of balls are drawn at random without replacement successively,until the bag is empty. If the number of ways in which each pair consists of one white and one black ball is $14400$,then $n$ is equal to