Permutations an...

If $$n$$ is an integer greater than $$1$$, then $$a-{ _{  }^{ n }{ C } }_{ 1 }(a-1)+{ _{  }^{ n }{ C } }_{ 2 }(a-2)+....+{ (-1) }^{ n }(a-n)$$ is equal to

Choose $$3, 4, 5$$ points other than vertices respectively on the sides $$AB, BC$$ and $$CA$$ of a $$\triangle ABC$$. The number of triangles that can be formed by using only these points as vertices, is

Total number of words that can be formed using all letters of the word $$\text{BRIJESH}$$ that neither begins with $$I$$ nor ends with $$B$$ is equal to.

If $$\alpha ,\beta , \gamma $$ are three consecutive integers. If these integers are raised to first, second and third positive powers respectively, and added then they form a perfect square, the square root of which is equal to the sum of these integers. Also, $$\alpha < \beta < \gamma $$. Then, $$\gamma$$ is equals to:

If $$^{n}C_{15} = ^{n}C_{8}$$, then the value of $$^{n}C_{21}$$ is

What was the bus charge per student?

The value of $$^{50}C_4+\displaystyle\sum^{6}_{r=1}$$ $$^{56-r}C_3$$ is?

A village has $$10$$ players. A team of $$6$$ players is to be formed. $$5$$ members are chosen first out of these $$10$$ players and then the captain from the remaining players. Then the total number of ways of choosing such teams is

An alphabet contains a $$A^{'s}$$ and b $$ B^{'s}$$ . (In all a+b letters ). The number of words each containing all the $$ A^{'s}$$ and any number of $$ B^{'s}$$, is 

The maximum number of intersection points of n circles and n straight lines , among themselves  is 80.The value of n is