TITLE: New Year Maths $2019$
QUESTION [23 upvotes]: $$\;\;\;\color{red}{\binom {20}{19}}\\
\color{orange}{+\binom {19}{a}
+{\binom  ab}}\\
\color{green}{+\binom bc
+\binom cd}\\
\color{blue}{+\binom de+
\binom ef}\\
\color{purple}{+\binom fg+\binom gh}\\
\color{magenta}{+\binom hk}\\[15pt]
\color{orange}=\\[10pt]
\color{red}{2019}\\[15pt]
\color{orange}{a,b,}
\color{green}{c,d,}
\color{blue}{e,f,}
\color{purple}{g,h,}
\color{magenta}k\color{orange}{=?}\\[20pt]$$
$$\color{red}{\text{Happy New Year!}}$$

Note - Please feel free to post any other interesting identities based on the same theme!

REPLY [10 votes]: $$\begin{align}&{7\choose H}+\color{red}{9\choose A}+\color{blue}{11\choose P}+{\color{blue}{12\choose P}}+\color{green}{13\choose Y}+\\
&{8\choose N}+\color{magenta}{16\choose E}+{15\choose W}+\\
&\color{green}{14\choose Y}+\color{magenta}{17\choose E}+\color{red}{10\choose A}+\binom{18}{R}=
2019.\end{align}$$

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