Determine the number of nonnegative integer solutions of the equation $x+y+z+t=98$.

Question

Determine the number of nonnegative integer solutions of the equation $x+y+z+t=98$.

Dear ones, please indicate a method or suggestion to solve. Thanks.

Answer 1

So to find the number of solutions to $x+y+z+t=98$, I'll use a method called stars and bars. Let's say that there are 98 stars (because the x,y,z, and t has to add up to $98$). And then there are 3 bars to divide the stars into four sections. Each of the sections corresponds to a value of x,y,z, and t. The number of ways to arrange $98$ stars and $3$ bars would be $101\choose3$.

Here is a little more insight into the topic. {How to use stars and bars?}