The number of natural numbers less than $1000$,in which no two digits are repeated,is:

Find the number of ways of arranging $6$ red balls and $6$ black balls in a row such that no two black balls are together.

How many words,with or without meaning,can be formed using the letters of the word $MONDAY$,assuming that no letter is repeated,if $4$ letters are used at a time?

The number of arrangements of the letters of the word $MANAMA$ in which two $M$'s do not appear adjacent 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

The number of four-digit even numbers that can be formed using the digits $0, 1, 2,$ and $3$ without repetition is: