See Theorem one in this Wikipedia article.
But it is not matching with the answer given.
By using that theorem, it would taken two from 10 available gaps, 10C2.
But i have the answer as 13c11.
I think they are considering it as X1,X2,X3 >=0. So we can have 13 gaps and 13C2 which is equal to 13C11.
I dont know whether my understanding is wrong , please correct.
How many solutions does this equation have: .
. . given
Consider an eleven-inch board marked in one-inch intervals.
. . . .
It can be divided into three nonzero pieces
. . by choosing any two of the ten inch-marks
. . and cutting the board there.
Therefore, there are: .