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Hey I have kind of a general question.
In my textbook, there are lots of questions that go something like this:
"Say we have 3 piles of balls, a blue pile, a red pile, and a yellow pile. Each pile has at least 8 balls. How many ways can we pick 8 balls from these three piles?"
(so for example in this case you could pick YYYYYYYY or BYYRRRRR, etc.)
In this case we use C(k+t-1,t-1) formula
But I'm stumped on ideas like this:
What if I take the above scenario, but this time the "blue pile" has only 2 balls, while the rest have 8. And I'd still like to pick 8 balls. I can't use the formula like normal because there are less options: for example BBBYYRRR isn't an answer as there are only 2 blue balls in the pile. Now let me go even further and say, there are only 2 blue balls, and only 3 red balls and only 4 yellow balls and I want to make a selection of 8 balls. I am completely stumped as to how to do this as I can't apply the normal formulas.
So I guess, is there a formula for when one of your sets is "limited"? Every single problem in the book the example is to make a k-element selection but the "sets" you are choosing from always have at least k elements in their set so you don't run into this problem.This is NOT a HW problem, this is just something I keep trying to figure out on my own. I am really, really poor at combination/permutation stuff so there is most likely a very easy answer to this I'm just not seeing.
In my textbook, there are lots of questions that go something like this:
"Say we have 3 piles of balls, a blue pile, a red pile, and a yellow pile. Each pile has at least 8 balls. How many ways can we pick 8 balls from these three piles?"
(so for example in this case you could pick YYYYYYYY or BYYRRRRR, etc.)
In this case we use C(k+t-1,t-1) formula
But I'm stumped on ideas like this:
What if I take the above scenario, but this time the "blue pile" has only 2 balls, while the rest have 8. And I'd still like to pick 8 balls. I can't use the formula like normal because there are less options: for example BBBYYRRR isn't an answer as there are only 2 blue balls in the pile. Now let me go even further and say, there are only 2 blue balls, and only 3 red balls and only 4 yellow balls and I want to make a selection of 8 balls. I am completely stumped as to how to do this as I can't apply the normal formulas.
So I guess, is there a formula for when one of your sets is "limited"? Every single problem in the book the example is to make a k-element selection but the "sets" you are choosing from always have at least k elements in their set so you don't run into this problem.This is NOT a HW problem, this is just something I keep trying to figure out on my own. I am really, really poor at combination/permutation stuff so there is most likely a very easy answer to this I'm just not seeing.