An experiment involves 3 red balls, 2 green balls and 4 yellow balls. How many distinct groups of three can be formed?
Asked
Active
Viewed 58 times
0
-
2Assuming that each of the balls are otherwise indistinguishable except by color, ask yourself instead the question of how many ways you can have three balls if there were an unlimited number of each ball available. Then recognize that the only group of balls you just counted that wasn't valid for your original problem was the group with nothing but green balls in it. – JMoravitz Sep 16 '17 at 01:22
-
As for counting that other problem, see stars and bars on wikipedia. – JMoravitz Sep 16 '17 at 01:23
-
Thanks @JMoravitz I am actually not interested in this particular experiment but I was using at as an analogy to something slightly more complicated. The problem I have with the stars and bars logic is that in a way it assumes that I only have two possible input but does not allow me to add further constraints. Consider the example on the wikipedia page - the question for me is how many (n-2) cells containing 1 element, 1 cell containing 2 elements and 1 cell containing 0 elements I can form from an n-element sequence. All elements and cells are distinguishable – Moe Sep 16 '17 at 02:46
-
@ZachBoyd I've been experimenting with combinations of stars and bars logic, but have not been able arrive to the answer I'm looking for. – Moe Sep 16 '17 at 02:48
-
Please edit your question to show us what you have attempted and state where you are stuck. – N. F. Taussig Sep 16 '17 at 08:51
-
The number of combinations can be found using generating functions. – Jens Sep 19 '17 at 18:27