## #solutions to constraint equation with binomial coefficients

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### #solutions to constraint equation with binomial coefficients

Hi,

Can someone explain how to find the number of solutions to an equation of the form

a1 + a2 + ... + an = x

possibly with constraints such as a1 > w or a2 < z where a1, a2, ... an and w, x, z etc. are nonnegative integers.

I am given to understand the solution can be found with binomial coefficients.
rsood

Posts: 2
Joined: Wed Aug 07, 2013 12:05 am

rsood wrote:Can someone explain how to find the number of solutions to an equation of the form

a1 + a2 + ... + an = x

As posted, the value of x is the sum of the n values ai.

rsood wrote:possibly with constraints such as a1 > w or a2 < z where a1, a2, ... an and w, x, z etc. are nonnegative integers.

What is the source of these constraints? How do they change what you're doing (summing n numbers) with the original equation?

stapel_eliz

Posts: 1797
Joined: Mon Dec 08, 2008 4:22 pm