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?

If all the numbers which are greater than $6000$ and less than $10000$ are formed with the digits $3, 5, 6, 7, 8$ without repetition of the digits,then the difference between the number of odd numbers and the number of even numbers among them is

$A$ number is called a palindrome if it reads the same backward as well as forward. For example,$285582$ is a six-digit palindrome. The number of six-digit palindromes,which are divisible by $55$,is ...... .

The number of ways in which four letters of the word '$MATHEMATICS$' can be arranged is given by

$A$ 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 total number of three-digit and five-digit integers which can be formed by using the digits $0, 1, 2, 3, 4, 5$,using each digit not more than once in each number,is: