Permutations an...

Sum of series : $$\sum_\limits{r=1}^n (r^2+1)( r! )$$ is _______

There are infinite, alike, blue, red, green and yellow balls. Find the number of ways to select $$10$$ balls.

Let $$(1+x)^n=C_0+C_1x+C_2x^2+.....+C_nX^n$$. (where $$C_r=^nC_r$$)
On the basis of given information, answer the following question.
$$C_1-3(C_3)+5(C_5)-7(C_7)+$$_______ is?

Maximum number of common chords of a parabola and a circle can be equal to

In a certain examination paper, there are $$n$$ question. For $$j = 1, 2....n$$, there are $$2^{n-j}$$ students who answered $$j$$ or more questions wrongly. If the total number of wrong answers is $$4095$$, then the value of $$n$$ is:

How many $$10-digit$$ numbers can be formed by using the digits $$1$$ and $$2$$?

The value of $$\displaystyle\sum^{10}_{r=0}(r)$$ $$^{20}C_r$$ is equal to?

What is the value of $$^nC_n$$?

Let $$S$$ be the set of $$6$$ digits numbers $$a_{1},a_{2},a_{3},a_{4},a_{5},a_{6}$$ (all digits distinct) where $$a_{1}>a_{2}>a_{3}<a_{4}>a_{5}<a_{6}$$. Then $$n(S)$$ is equal to

A library has $$'a'$$ copies of one book, $$'b'$$ copies of each of two books, $$'c'$$ copies of each of three books, and single copy each of $$'d'$$. The total number of ways in which these books can be arranged in a row is