Combinatorial Analysis
The amounts of possibilities to select k out of n elements are calculated, setting value on sequence or not (i.e. arrangement or combination), and permitting repetitions or not.
Example:
n = 49 k = 6 Arrangements without repetit. = 10 068 347 520 Arrangements with repetitions = 13 841 287 201 Combinations without repetit. = 13 983 816 Combinations with repetitions = 25 827 165 Permutations of k : k! = 720
Formulas:
Disorderd (Combinations) 
Ordered (Variations) 
Ordered and k=n (Permutations) 

Without repetitions 


With repetitions 