Permutations an...

In how many ways a garland can be made from exactly $$10$$ flowers

The figure is given.

In how many way can $$12$$ gentlemen sit around a round table so that three specified gentlemen are always together.

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

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:

Find the missing number in the circle:

Find the missing number in above figure :

Find the missing number in above figure :