# Equations relating combinations

Suppose that a, b, and c are integer numbers, and that there are a many unique combinations of length b, where each constituent of the combination has c permutations, and suppose that combinations which would be the same if not for being in a different order are ignored as duplicates (e.g. where d, e, and f are constituents of a combination, combination def would be thrown out as a duplicate of fed but fed would be still be considered). What are the equations which relate a, b, and c?

• I've made some changes, I hope it is a little clearer now. I'm not the best at explaining. – tom894 Aug 29 '19 at 17:49
• Combinations are generally combinations of some things. What things are you putting into whatever you think a “combination of length $b$” is? Are you making combinations of the letters $d,e,f$ only? What are examples of some of the $c$ permutations of one of these constituents? As far as I know, the letter $d$ has only one permutation. – David K Aug 29 '19 at 21:12
• Perhaps it would be best to give a very concrete example of what you’re doing: pick a small number $b$ and write out a list of every unique combination of length $b.$ Then write out a list of all $c$ permutations of whatever it is you’re permuting. Then people might be able to see what you mean. Right now I think the technical words are getting in the way. – David K Aug 29 '19 at 21:16

Are you considering combinations and permutations of $$b$$ distinct objects from a total of $$N$$ distinct objects? If so:-
$$a=\begin{pmatrix} N \\ b \end{pmatrix}$$ and $$c=b!$$