I have a simple question from text-book about this subject to see if I got it right.
Say I have a natural number below 1000, and I need to find all combinations of it's digits that their sum will be 14.
Now it basically:
0<=x1,x2,3<=9, with x1 + x2 + x3 = 14.
Going the inclusion - exclusion way, the solution seems to be:
|U| = D(3,14) |S1|=|S2|=|S3| = D(3,4)
So the answer:
|U|-|S1|+|S2|-|S3| = D(3,14) - D(3,4)
Seems a bit too easy, can anyone comments