Find the number of integral solutions of $\large 2x + y + z = 20$ with $x, y, z \ge 0$ ?
I saw a method of generating function but i donot have knowledge about generating function any alternative way to solve this , answer = 121
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$y+z=20-2x$ is one of $20,18,16,\cdots0$, so that there are $$21+19+17+\cdots1=121$$ solutions.
true blue anil
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very compact form sir please explain a bit – sumit goyal Feb 02 '18 at 17:08
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@sumitgoyal: what don't you understand ? – Feb 02 '18 at 17:18
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no i dont got you y+z is one of ?? you didnot took x in consideration ? sir – sumit goyal Feb 02 '18 at 17:20
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@sumitgoyal: I just used $y+z=20-2x$ and assigned $x$ all the values it can take. – Feb 02 '18 at 17:22
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https://math.stackexchange.com/questions/2017905/find-the-number-of-integral-solutions-of-2x-y-z-20?rq=1 i found same question here , can you explain how to use star and bars sir – sumit goyal Feb 02 '18 at 17:25
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got it thanku.,,, – sumit goyal Feb 02 '18 at 17:29