The number of positive integral solutions of $abc = 30$ is

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

If $\alpha$ represents the number of arrangements of $p$ men and $q$ women in a row such that all men are together and $\beta$ represents the number of circular arrangements of the same people with the same condition,then $\alpha: \beta$ is

$A$ $5$-digit number $\overline{abcde}$,when multiplied by $9$,gives the $5$-digit number $\overline{edcba}$. The sum of the digits in the number is:

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

The number of $3$-digit numbers,formed using the digits $2, 3, 4, 5$ and $7$,when the repetition of digits is not allowed,and which are not divisible by $3$,is equal to ..........