Given:
- Set of size
n - Select elements (unordered, no duplicates) from that set
- Select
kelements, for whichmin <= k < max
Question: How many k-combinations are there?
If k were a fixed number, wikipedia has the answer: n! / (k! (n-k)!)
Unfortunately, it's not.
For example:
- Given the set
[A, B, C, D, E], select at least2and at most3elements. - So
n=5,min=2,max=4,2 <= k < 4. - Number of combinations:
6!/2!4! + 6!/3!3! = 720/48 + 720/36 = 35
So 35 combinations. What's the general formula given n, min, max?
k < maxrather thank <= max? – Henry May 06 '14 at 22:396!/2!4! + 6!/3!3! = 7!/3!4!– Henry May 06 '14 at 22:40k <= maxis fine too. As for the sum, at least then!/(min! (n-max)!)can be extracted? – Geoffrey De Smet May 07 '14 at 06:14