$10$ different letters of English alphabet are given. Out of these letters, words of $5$ letters are formed. How many words are formed when at least one letter is repeated
$99748$
$98748$
$96747$
$97147$
A group of students comprises of $5$ boys and $n$ girls. If the number of ways, in which a team of $3$ students can randomly be selected from this group such that there is at least one boy and at least one girl in each team, is $1750$, then $n$ is equal to
The number of ways of dividing $52$ cards amongst four players so that three players have $17$ cards each and the fourth player just one card, is
In how many ways can a student choose a programme of $5$ courses if $9$ courses are available and $2$ specific courses are compulsory for every student?
The numbers of permutations of $n$ things taken $r$ at a time, when $p$ things are always included, is
A set contains $(2n + 1)$ elements. The number of sub-sets of the set which contains at most $n$ elements is :-