New Year Maths $2019$ $$\;\;\;\color{red}{\binom {20}{19}}\\
\color{orange}{+\binom {19}{a}
+{\binom  ab}}\\
\color{green}{+\binom bc
+\binom cd}\\
\color{blue}{+\binom de+
\binom ef}\\
\color{purple}{+\binom fg+\binom gh}\\
\color{magenta}{+\binom hk}\\[15pt]
\color{orange}=\\[10pt]
\color{red}{2019}\\[15pt]
\color{orange}{a,b,}
\color{green}{c,d,}
\color{blue}{e,f,}
\color{purple}{g,h,}
\color{magenta}k\color{orange}{=?}\\[20pt]$$
$$\color{red}{\text{Happy New Year!}}$$

Note - Please feel free to post any other interesting identities based on the same theme!
 A: $$\color{red}{\binom {20}{19}}
+\color{orange}{\binom {19}{16}
+{\binom  {16}{14}}}+ 
\color{green}{\binom {14}{12}
+\binom {12}{7}}+
\color{blue}{\binom {7}{6}+
\binom {6}{5}}+
\color{purple}{\binom {5}{3}+\binom {3}{1}}+
\color{magenta}{\binom {1}{0}}
=\color{red}{2019}$$

A: $$\color{red}{\binom{20}{19}}+\color{orange}{\binom{19}{18}}+\color{orange}{\binom{18}{17}}+\color{green}{\binom{17}{16}}+\color{green}{\binom{16}{12}}+\color{blue}{\binom{12}{11}}+\color{blue}{\binom{11}{10}}+\color{purple}{\binom{10}{8}}+\color{purple}{\binom{8}{5}}+\color{magenta}{\binom{5}{0}}\color{orange}=\color{red}{2019}$$
$\color{red}{\text{Happy New Year!}}$
A: $$\begin{align}&{7\choose H}+\color{red}{9\choose A}+\color{blue}{11\choose P}+{\color{blue}{12\choose P}}+\color{green}{13\choose Y}+\\
&{8\choose N}+\color{magenta}{16\choose E}+{15\choose W}+\\
&\color{green}{14\choose Y}+\color{magenta}{17\choose E}+\color{red}{10\choose A}+\binom{18}{R}=
2019.\end{align}$$

 $\binom76+\binom85+\binom98+\binom{10}8+\binom{11}{10}+\binom{12}{10}+\binom{13}{12}+\binom{14}{12}+\binom{15}{13}+\binom{16}{14}+\binom{17}{14}+\binom{18}{15}=2019.$ 

A: $\color{red}{{20 \choose 19}+{19\choose 16}}+\color{orange}{{16\choose 3}+{3\choose 1}}+\color{green}{{1\choose 2}+{2\choose 2}}+\color{blue}{{2\choose 466}+{466\choose 465}}+\color{purple}{{465\choose 466}+{466\choose 467}}=\color{magenta}{2019}$.
