Find the number of integer solutions x1+x2+x3=20 with x1≥0 x2≥1 x3≥1
is this C(20,2)?
Thank you.
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The number of way to put N 1's into K variables is $\displaystyle \tbinom{N+K-1}{N}$.
If we want $\displaystyle x_2\ge 1~\&~x_3\ge 1$ we can think of putting a 1 into each of those two variables.
So is the answer $\displaystyle \tbinom{18+3-1}{18}~?$