Expert: Sherry Wallin - 7/17/2011

Question
how many combinations are there if you have two groups of numbers.1-50 then also 1-11

Answer
Combinations imply that 1,2 is no different than 2,1 or abc is no different than cab etc, exact repeats not allowed
You have really only 50 unique elements and they are 1,2,...,50

I am interpreting your question to mean how many sets can I get from 1,2,...,50 not including the empty set, i.e., subsets of 1,2,...,50.
How many individual elements are there? Yes there are 50
How many pairs are there? Please don't say 26 because just to list a few 1,2 1,3 1,4 1,5 1,6,...1,50 here are 49 but since you also through in 1-11 1,1 belongs in there as well but we wouldn't count 1,2 1,3,...,1,11 again because they are repeats
How many triplets are there? This will become more tedious and difficult to try to list so please notice that another way to see how many pairs there were is to find 50C2 = 50!/2!48! = 50*49*48!/2*1*48! = 50*49/2 = 25*49 = 1225 but don't forget the 'other' pairs which are 1,1 2,2 3,3 ... 11,11 so you really have 1236 pairs

Now back to triplets 50C3 = 50!/3!47! = 50*49*48*47!/3*2*1*47! = 50*49*48/6 = 19600 but we need to somehow count the 'other' triplets that can be made from 1-11, i.e., 1,1,1   2,2,2   3,3,3 ... 111,111, 111 but there is also 1,1,x where x is any of 2-11 and 2,2,x where x is any of 1,3-11
and so on and so forth.

I'l let you think on this some more and if you need more help send it my way but tell me what you've done and tried

Math Prof