Permutations an...

There are $$31$$ objects in a bag in which $$10$$ are identical, then the number of ways of choosing $$10$$ objects from bag is?

The coefficient of $$x^{18}$$ in the expansion of $$(1+x)(1-x)^{10}\{(1+x+x^2)^9\}$$ is?

A team of three persons with at least one boy and atleast one girl is to be formed from $$5$$ boys and $$n$$ girls. If the number of sum teams is $$1750$$, then the value of $$n$$ is

If $$\dfrac{1}{6!}+\dfrac{1}{7!}=\dfrac{x}{8!}$$, then $$x=?$$

$$^{36}C_{34}=?$$

$$\dfrac{^nC_r}{^nC_{r-1}}=?$$

There are $$10$$ points in a plane, out of which $$4$$ points are collinear. The number of line segments obtained from the pairs of these points is?

If $$^{n}C_3=220$$, then $$n=?$$

If $$^nC_{10}={^{n}C_{14}}$$, then $$n=?$$

If $$^{n}C_r+{^nC_{r+1}}={^{n+1}C_x}$$, then $$x=?$$