I have balls of k different colors. We have an infinite supply of balls for each color. I want to select n balls(1<=k<=n). How many ways are there i.e how many combinations(not arrangements) are there such that atleast 1 ball of each color is selected.
example if n=10 and k=10 , answer =1
Please note that this is not a homework assignment and i am not asking any ready made solutions. Just some guidance.
Thank you very much for your reply and thanks for pointing out that my question was incomplete( i have edited it now)
Can you please guide me how you came up with that formula. I am really bad at combinatorics. So i would be glad if you could just point some learning material on the net for the above problem( or you could just point what search string to use in google, right now i am using "combinatorics" only)
Thanks for your help.
This is a typical problem that is part of the general topic: “Occupancy Problems”.
There is a whole list of formulae, there are two used in your question.
Consider: “How many ways can N identical objects into k different cells?”
The answer is . But that allows some cells to be empty.
If, as in your case, no cell can be empty, then the answer is .