$$\text { If } 10{ }^n C_2=3^{n+1} C_3 \text {, then the value of } n \text { is }$$

There are 10 points in a plane, out of these 6 are collinear. If $$N$$ is the total number of triangles formed by joining these points, then $$N=$$

In an examination, the maximum marks for each of three subjects is $$n$$ and that for the fourth subject is $$2 n$$. The number of ways in which candidates can get $$3 n$$ marks is

If a set $$A$$ has $$m$$-elements and the set $$B$$ has $$n$$-elements, then the number of injections from $$A$$ to $$B$$ is