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?

Consider a class of $5$ girls and $7$ boys. The number of different teams consisting of $2$ girls and $3$ boys that can be formed from this class,if there are two specific boys $A$ and $B$ who refuse to be members of the same team,is

In how many ways can $8$ identical balls be distributed into $3$ distinct boxes such that no box remains empty?

If $^{n-1}C_r = (k^2 - 3) \cdot ^nC_{r+1}$,then an interval containing the values of $k$ is

$A$ man has $7$ friends. In how many ways can he invite one or more of them for a tea party?

The total number of ways of selecting $4$ letters from all the letters of the word $TSEAMCET$ is