In how many ways can a team of $11$ members be formed from a group of $15$ persons?

Find the total number of $9$ digit numbers which have all the digits different.

There are two urns. Urn $A$ has $3$ distinct red balls and urn $B$ has $9$ distinct blue balls. From each urn,two balls are taken out at random and then transferred to the other. The number of ways in which this can be done is

How many different words can be formed with the letters of the word '$BHARAT$'? In how many of these are $B$ and $H$ never together?

The number of positive integral solutions of $a \cdot b \cdot c = 30$ is

On the sides $AB, BC, CA$ of a $\Delta ABC$,$3, 4, 5$ distinct points (excluding vertices $A, B, C$) are respectively chosen. The number of triangles that can be constructed using these chosen points as vertices are: