The number of all possible positive integral solutions of the equation $xyz=30$ is

The number of times the digit $3$ will be written when listing the integers from $1$ to $1000$ is

Let $x$ denote the number of ways of arranging $m$ boys and $m$ girls in a row so that no two boys sit together. If $y$ and $z$ denote the number of ways of arranging $m$ boys and $m$ girls in a row and around a circular table respectively so that boys and girls sit alternately,then $x: y: z=$

If ${}^n P_r = 30240$ and ${}^n C_r = 252$,then the ordered pair $(n, r)$ is equal to

The number of $4$-letter permutations formed using the English alphabet such that the number of distinct vowels is equal to the number of distinct consonants,when repetition is allowed,is

$A$ 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