If the number of five-digit numbers with distinct digits and $2$ at the $10^{\text{th}}$ place is $336k$,then $k$ is equal to

Eight different letters of an alphabet are given. Words of four letters from these are formed. The number of such words with at least one letter repeated is:

In how many ways can $5$ speakers $S_1, S_2, S_3, S_4$,and $S_5$ give speeches one after the other if $S_3$ must speak after both $S_1$ and $S_2$?

How many numbers can be formed using the digits $1, 2, 3, 4$ if repetition of digits is not allowed?

The number of arrangements of the word $KANGAROO$ in which $A$'s do not appear together is

$5$-digit numbers are to be formed using $2, 3, 5, 7, 9$ without repeating the digits. If $p$ is the number of such numbers that exceed $20000$ and $q$ is the number of those that lie between $30000$ and $90000$,then $p : q$ is