I am spinach $__$

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

I want to put the \(\color{Blue}{\text{Blue bag}}\) and the \(\color{Red}{\text{Red bag}}\) in a \(\color{Purple}{\text{Purple bag}}\) 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 \(\color{Purple}{\text{Purple bag}}\) ?

Details and assumptions:-

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

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

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

This problem is part of the set Vegetable Combinatorics


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