As a programmer, I frequently need to be able to know the how to calculate the number of permutations of a set, usually for estimation purposes.
There are a lot of different ways specify the allowable combinations, depending on the problem at hand. For example, given the set of letters A,B,C,D
Assuming a 4 digit result, how many ways can those letters be arranged?
What if you can have 1,2,3 or 4 digits, then how many ways?
What if you are only allowed to use each letter at most once? twice?
What if you must avoid the same letter appearing twice in a row, but if they are not in a row, then twice is ok?
Etc. I'm sure there are many more.
Does anyone know of a web reference or book that talks about this subject in terms that a non-mathematician can understand?
Thanks!
Assuming a 4 digit result, how many ways can those letters be arranged?
when picking the 1st digital , you have 4 choices ,which is one of A, B , C and D ; it is the same when picking the 2nd, 3rd ,4th since repetition is allowed:
so you have total : 4*4*4*4 = 256 choices.
What if you can have 1,2,3 or 4 digits, then how many ways?
It is easy to deduce from question 1.
What if you are only allowed to use each letter at most once?
When pick the 1st digital , you have 4 choices ,which is one of A , B , c and D ; when picking the 2nd , you have 3 choice except the one you have picked for the 1st ; and 2 choices for 3rd , 1 choices for the 4th.
So you have total : 4 * 3 * 2 * 1 = 24 choice.
The knowledge involving here include combination , permutation and probability. Here is a good tutorial to understand their difference.