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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- Nov 14th 2011, 02:34 PMtinabakerFind the number of integer solutions
Find the number of integer solutions x1+x2+x3=20 with x1≥0 x2≥1 x3≥1

is this C(20,2)?

Thank you.

- Nov 14th 2011, 02:54 PMTKHunnyRe: Find the number of integer solutions
How did you get that result?

Take y2 = x2 - 1 and y3 = x3 - 1

Rephrase to x1 + (y2 + 1) + (y3 + 1) = 20 or x1 + y2 + y3 = 18

And out pops C(18+2,2). I think you have it! - Nov 14th 2011, 03:03 PMPlatoRe: Find the number of integer solutions
When posting please do not use special fonts.

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 $\displaystyle \tbinom{18+3-1}{18}~?$ - Nov 14th 2011, 03:06 PMtinabakerRe: Find the number of integer solutions
thank you for your help :)

- Nov 24th 2011, 05:52 PMCaramelCardinalRe: Find the number of integer solutions
If you require all x's to be 0 or greater, the equation is ((N-1)C(K-1)).