Permutations an...

Let $$ S= \left\{1,2,3,.......n\right\} $$ and $$ A =\left\{(a, b) \left. \right | 1 \geq a, b \geq n\right\} = S \times S\: $$. A subset $$ B$$ of $$A $$ is said to be a good subset if $$ (x, x) \in B$$ for every $$x \in S.$$ Then the number of good subsets of $$A$$ is

If $$(1+x)^n=C_0+C_1x+C_2x^2+ ......+C_nx^n,$$ then the value of $$C_0 + 2C_1+ 3 C_2 + ...... (n + 1) C_n$$ will be

Forty teams play a tournament. Each of them plays with every other team just once. Each game result is a win for one team. If each team has a $$50\%$$ chance of winnings each game, the number of ways such that at the end of the tournament, every team has won a different number of games is:

The sum of the series $$\displaystyle \sum_{r=0}^{10} {\;}^{20}C_r$$ is

There are 8 buses running from Kota to Jaipur and 10 buses running from Jaipur to Delhi. In how many ways a Person can travel from Kota to Delhi via Jaipur by bus?

If $$\displaystyle^{n}P_{r}=  360$$  and  $$^ {n}C_{r}=15$$ then find the value of r

The value of $$\displaystyle ^{ 19 }C_{ 18 }+^{ 19 }C_{ 17 }$$

IF$$\displaystyle ^{n}C_{r}=^{n}P_{r}$$  then r can be____

Different calenders for the month of February are made so as to serve for all the coming years. The number of such calenders is

Find the value of $$\displaystyle ^{10}C_{10}$$