[Math] New Year Maths $2019$

Question

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

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

Answer 1

$$\color{red}{\binom {20}{19}} +\color{orange}{\binom {19}{16} +{\binom {16}{14}}}+ \color{green}{\binom {14}{12} +\binom {12}{7}}+ \color{blue}{\binom {7}{6}+ \binom {6}{5}}+ \color{purple}{\binom {5}{3}+\binom {3}{1}}+ \color{magenta}{\binom {1}{0}} =\color{red}{2019}$$