I am spinach $__$

There are 17 raw spinach leaves\color{LimeGreen}{\textbf{17 raw spinach leaves}} in a Blue bag\color{Blue}{\text{Blue bag}} and 19 ripe spinach leaves\color{Green}{\textbf{19 ripe spinach leaves}} in a Red bag\color{Red}{\text{Red bag}}.

I want to put the Blue bag\color{Blue}{\text{Blue bag}} and the Red bag\color{Red}{\text{Red bag}} in a Purple bag\color{Purple}{\text{Purple bag}} after removing at least one (and maximum all) leaves from each of the 2 bags.

Then how many different possibilities are there for the contents of the Purple bag\color{Purple}{\text{Purple bag}} ?


Details and assumptions:-

\bullet The contents of the Purple bag\color{Purple}{\text{Purple bag}} are counted in terms of (Red,Blue)\color{Red}{(Red,}\color{Blue}{Blue)}.

\bullet If i remove 3 leaves from Blue bag\color{Blue}{\text{Blue bag}} and 4 leaves from the Red bag\color{Red}{\text{Red bag}}, then the Purple bag\color{Purple}{\text{Purple bag}} will have the contents (Red,Blue)=(15,14)\color{Red}{(Red,}\color{Blue}{Blue)} = (15,14).

(3\color{LimeGreen}{3} out of 17 raw leaves\color{LimeGreen}{\text{17 raw leaves}} and 4\color{Green}{4} out of 19 ripe leaves\color{Green}{\text{19 ripe leaves}} were removed)


This problem is part of the set Vegetable Combinatorics

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