I am spinach $__$

There are 17 raw spinach leaves \color{limegreen}{\textbf{17 raw spinach leaves}} in a Blue bag \color{#3D99F6}{\text{Blue bag}} and 19 ripe spinach leaves \color{#20A900}{\textbf{19 ripe spinach leaves}} in a Red bag \color{#D61F06}{\text{Red bag}} .

I want to put the Blue bag \color{#3D99F6}{\text{Blue bag}} and the Red bag \color{#D61F06}{\text{Red bag}} in a Purple bag \color{#69047E}{\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{#69047E}{\text{Purple bag}} ?


Details and assumptions :-

\bullet The contents of the Purple bag \color{#69047E}{\text{Purple bag}} are counted in terms of ( R e d , B l u e ) \color{#D61F06}{(Red,}\color{#3D99F6}{Blue)} .

\bullet If i remove 3 leaves from Blue bag \color{#3D99F6}{\text{Blue bag}} and 4 leaves from the Red bag \color{#D61F06}{\text{Red bag}} , then the Purple bag \color{#69047E}{\text{Purple bag}} will have the contents ( R e d , B l u e ) = ( 15 , 14 ) \color{#D61F06}{(Red,}\color{#3D99F6}{Blue)} = (15,14) .

( 3 \color{limegreen}{3} out of 17 raw leaves \color{limegreen}{\text{17 raw leaves}} and 4 \color{#20A900}{4} out of 19 ripe leaves \color{#20A900}{\text{19 ripe leaves}} were removed)


This problem is part of the set Vegetable Combinatorics


The answer is 323.

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2 solutions

Tasmeem Reza
Jul 27, 2014

R e d b a g \color{#D61F06}{Red\: bag} can contain from 0 0 to 16 16 leaves, thus 17 17 possibilities

B l u e b a g \color{#3D99F6}{Blue\: bag} can contain from 0 0 to 18 18 leaves, thus 19 19 possibilities

According to the M u l t i p l i c a t i o n R u l e Multiplication\: Rule of Combinatorics we have 17 × 19 = 323 17\times19=\boxed{323} possibilities

Another very similar way of thinking about this is you can take 1 17 1-17 leaves from the red bag \color{#D61F06}{\text{red bag}} and 1 19 1-19 leaves from the blue bag \color{#3D99F6}{\text{blue bag}} , hence you have 17 19 = 323 17\cdot 19=\boxed{323} possibilities.

mathh mathh - 6 years, 10 months ago

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This one is the easiest of this set ...

Aditya Raut - 6 years, 10 months ago

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Then why does it has a level 4 ratings? I think it's very elementary

Christopher Boo - 6 years, 10 months ago

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@Christopher Boo Just because it's elementary, doesn't mean that it's very easy, XD

Samuraiwarm Tsunayoshi - 6 years, 10 months ago

@Christopher Boo Completely Agreed Christiiieeee !

Aditya Raut - 6 years, 10 months ago
Cody Johnson
Jul 29, 2014

Generating functions.

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