# How many maximum combinations can be found without repeating characters, from a,b,c,d?

I manually calculated that 11 combinations can be made, but I don't know how to do it by maths-formula.

I thought 12 combinations can be made if I apply permutations and combinations as '4C2'= 12.

I found combinations as

2) abc,bcd,abd,acd.

3)abcd.

but these are only 11, Am I missing something or How to calculate it mathematically?

• Welcome to MSE. Here's some guide to write math in MathJax. Jun 20, 2018 at 14:26
• This is not a permutations question unless the order of selection matters. Jun 21, 2018 at 9:22

First note that what you call $4C2$ should come out equal to six, which is the number of combinations of two different letters chosen from four. Various notation is used in different places for the same thing - $^4C_2$ can be used, but most common here (and conveniently available using "\binom 42" with dollar signs instead of quotation marks) is $\binom 42$
As for the answer, each letter can either be included or excluded in the combination, which gives a total of $2^4=16$ possibilities. You have missed out the possibility of no letters at all (which you may not have wanted anyway) and also the four single letters - with the eleven you did find, that gives all sixteen possibilities.