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# Find number of solutions of a linear equation of n variables

Given a linear equation of n variables, find number of non-negative integer solutions of it. For example,let the given equation be “x + 2y = 5”, solutions of this equation are “x = 1, y = 2”, “x = 5, y = 0” and “x = 1. It may be assumed that all coefficients in given equation are positive integers.

**Example :**

```
Input:  coeff[] = {1, 2}, rhs = 5
Output: 3
The equation "x + 2y = 5" has 3 solutions.
(x=3,y=1), (x=1,y=2), (x=5,y=0)

Input:  coeff[] = {2, 2, 3}, rhs = 4
Output: 3
The equation "2x + 2y + 3z = 4"  has 3 solutions.
(x=0,y=2,z=0), (x=2,y=0,z=0), (x=1,y=1,z=0)
```

```java
class Solution {
    public static int countSol(int[] coeff, int n, int rhs) {
        int[] dp = new int[rhs + 1];
        dp[0] = 1;
        for (int i = 0; i < n; i++)
            for (int j = coeff[i]; j <= rhs; j++)
                dp[j] += dp[j - coeff[i]];

        return dp[rhs];
    }
}
```