The number of five-digit numbers greater than $50000$ that can be formed by using all the digits $0, 1, 3, 5, 9$ only once is

$A$ coin is tossed $3$ times and the outcomes are recorded. How many possible outcomes are there?

The letters of the word $COCHIN$ are permuted and all permutations are arranged in alphabetical order as in an English dictionary. The number of words that appear before the word $COCHIN$ is

$6$ boys and $5$ girls sit in a line such that $(I)$ no two girls sit together $(II)$ all the girls sit together. If $p$ is the number of arrangements in case $(I)$ and $q$ is the number of arrangements in case $(II)$,then $p/q =$

There are $10$ distinct letters of the English alphabet. Words of $5$ letters are formed using these letters. How many such words can be formed if at least one letter is repeated?

The number of different $9$-digit numbers that can be formed by rearranging the digits of the number $445577888$ such that the odd digits occupy even positions is: