I have searched the web for this answer and now must ask a community. Hello community. So say i can choose n
items out of a numbered list no higher than k
. So if i could choose 2 items from a list of 10 (1 - 10) then i would 100 possibilities. The probability, obviously, is 1/100.
Now things get tricky...,
There exists a constraint that the numbers must be in natural ordering. This is where i am getting to my first problem. I do not know how to calculate this (i have referenced several online combinatorics guides, they never seem to touch on this case). So if there is natural order required and n = 2
and k = 10
i will have to provide the probability i could guess the correct answer. This has been provided for me (this is not homework, this is my own self studying, but i am stumped!) which is 1/55
. 45 of the answers ({3, 2}, {7, 1}, ... etc, since 7 comes after 1, its not in natural ordering) are not allowed. So how would i calculate such this probability?
The second problem is what if i need to not only have natural ordering, but repetitions are not allowed? Then how would calculate that???
Now i am not just coming here as my first attempt. I have spent about 2 hours googling key words and reading articles trying to find such answers. I keep running into the same 4 problems/answers (Permutation: order matters, does not matter (not referring to natural ordering
) and Combination: Repetitions allowed, not allowed (but not combined in my case!)
Thank you very much. If you are confused on my question, please leave a comment.