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## Main Question or Discussion Point

**How are these two equal??(equation, inequality)**

I study discrete mathematics and we are doing combinations at the moment. There is this example in the book(Discrete Mathematics and Combinatorics p. 30 Ex. 1.43) where it states that the

**number of integer solutions**for:

x

_{1}+x

_{2}+x

_{3}+x

_{4}+x

_{5}+x

_{6}<10 where x

_{i}[tex]\geq[/tex]0

is equal to the number of integer solutions of

x

_{1}+x

_{2}+x

_{3}+x

_{4}+x

_{5}+x

_{6}+x

_{7}=10 where x

_{i}[tex]\geq[/tex]0 and x

_{7}>0

Can someone explain me this? The author supposes that I magically understand what goes through his mind.

Here is a screenshot of the problem: http://img251.imageshack.us/img251/823/garbageab.jpg [Broken]

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