I have this problem with combinations that requires one to make a group of 10 from 4 objects and one has many of each of these 4 distinct object types. This type of problem I believe would follow the Stars+Bars approach. But I have difficulty visualizing it this way.
So to make a context based example, say we have 4 veggies these being: S-spinach C-corn T-tomato B-broccoli
We have as many of these veggies that we need. So the addition to this problem is that we must have at least 1 Tomato and at least 2 Broccoli.
If the total amount of each veggies was finite, then one can do a product of Combinations(regular type of combination) Since we have this infinite amount of veggies then we use, i guess the formula: C(m+n-1,m), is now used for the Combinations, but this would mean we look at it from Bars and Stars way.
So an example possible list is: TBBXXXXXXX Where X represents any of the other veggies. Another: TTBBXXXXXX etc
So there is a lot of combinations to go thru when AT Least is fairly small. I guess one can do the inclusion-exclusion principle on this then.
But not fully certain how to go forward. Hope someone can help here.