Find the number of integer solutions of
1) x1 + x2 +x3 + x4= 15
x1 >1, x2 >0, x3 > 1, x4> 2
2) x1 + x2 + x3 + x4 =12
xi >0, i= 1,2,3,4.
Here's the second one . . .the easier of the two.
Find the number of integer solutions of: .
Consider 12 objects in a row; leave a space between them.
There are 11 spaces.
We choose 3 of them to insert "dividers."
So that: .
. . And: .
Therefore, there are: . solutions.