Permutations an...

Set of value of r for which, $$^{18}C_{r-2}+2\cdot {^{18}C_{r-1}}+{^{18}C_{r}} \geq {^{20}C_{13}}$$ contains?

The no.of triangles formed by selecting the points from Regular pentagon is 

$$^{n}C_{r}+2^{n}C_{r+1}+^{n}C_{r+2}$$ is equal to 

Value of $$\displaystyle \sum _{ r=0 }^{ n} r.\left(^{n}C_{r}\right)^{2}$$ is equal to

The no .of ways of selecting a prime numbers from First 10 natural numbers is 

A rectangle with sides 2m - 1 and 2n - 1 is divided into square of unit length by drawing parallel lines as shown in diagram, then the number of rectangles possible with odd side length is 

How many integers are there such that $$2 \le n \le 100$$ and the highest common factor of $$n$$ and $$36$$ is $$1$$?

If $$^mC_3+^mC_4>^{m+1}C_3$$, then least value of $$m$$ is :

The value of $$\left( \begin{matrix} 30 \\ 0 \end{matrix} \right) \left( \begin{matrix} 30 \\ 10 \end{matrix} \right) -\left( \begin{matrix} 30 \\ 1 \end{matrix} \right) \left( \begin{matrix} 30 \\ 11 \end{matrix} \right) +\left( \begin{matrix} 30 \\ 2 \end{matrix} \right) \left( \begin{matrix} 30 \\ 12 \end{matrix} \right) .....+\left( \begin{matrix} 30 \\ 20 \end{matrix} \right) \left( \begin{matrix} 30 \\ 30 \end{matrix} \right) $$ is, where $$\left( \begin{matrix} n \\ r \end{matrix} \right) =^{ n }{ C }_{ r }.$$

The number of ways in which $$9$$ persons can be divided into three equal groups, is