The number of integers between $10$ and $10,000$ such that in every integer every digit is greater than its immediate preceding digit,is

The number of ways in which a team of $11$ players can be formed out of $25$ players,if $6$ out of them are always to be included and $5$ of them are always to be excluded,is

If the total number of $m$-element subsets of the set $A = \{a_{1}, a_{2}, \ldots, a_{n}\}$ is $k$ times the number of $m$-element subsets containing $a_{4}$, then $n$ is

Out of $6$ boys and $4$ girls,a group of $7$ is to be formed. In how many ways can this be done if the group is to have a majority of boys?

$A$ student is to answer $10$ out of $13$ questions in an examination such that he must choose at least $4$ from the first $5$ questions. The number of choices available to him is

How many words of $4$ distinct letters can be formed using the letters of the word $DHOLPUR$ such that $L$ and $P$ are always included?