If $f(y) = 1 - (y - 1) + {(y - 1)^2} - {(y - 1)^{^3}} + ... - {(y - 1)^{17}},$ then the coefficient of $y^2$ in it is
$^{17}{C_2}$
$^{17}{C_3}$
$^{18}{C_2}$
$^{18}{C_3}$
The value of $^{4n}{C_0}{ + ^{4n}}{C_4}{ + ^{4n}}{C_8} + ....{ + ^{4n}}{C_{4n}}$ is
If the number of terms in the expansion of ${\left( {1 - \frac{2}{x} + \frac{4}{{{x^2}}}} \right)^n},x \ne 0$ is $28$ then the sum of the coefficients of all the terms in this expansion, is :
The value of ${\sum\limits_{r = 1}^{19} {\frac{{{}^{20}{C_{r + 1}}\left( { - 1} \right)}}{{{2^{2r + 1}}}}} ^r}$ is
$\sum_{\substack{i, j=0 \\ i \neq j}}^{n}{ }^{n} C_{i}{ }^{n} C_{j}$ is equal to
$\sum\limits_{n = 0}^4 {{{\left( {1009 - 2n} \right)}^4}\left( \begin{gathered}
4 \hfill \\
n \hfill \\
\end{gathered} \right)} {\left( { - 1} \right)^n}$ is