Let $5$-digit numbers be constructed using the digits $0, 2, 3, 4, 7, 9$ with repetition allowed,and are arranged in ascending order with serial numbers. Then the serial number of the number $42923$ is $...............$.

$A$ building has a ground floor and $10$ more floors. Nine persons enter a lift at the ground floor. The lift goes up to the $10$th floor. The number of ways in which any $4$ persons exit at a floor and the remaining $5$ persons exit at a different floor, if the lift does not stop at the first and the second floors, is equal to:

The number of natural numbers less than $10000$ which are divisible by $5$ and in which no digit is repeated is:

What is the total number of ways of choosing $4$ cards from a pack of $52$ playing cards? In how many of these are the four cards of the same suit?

$A$ question paper has $3$ parts and each part contains $4$ questions. The number of different ways in which a candidate can answer $8$ questions choosing at least two from each part is

${ }^{34} C_5+\sum_{r=0}^4{ }^{(38-r)} C_4=$