A. permutation

B. partial permutation

C. combination

D. partial permutation with repetition

E. combination with repetition

I am looking for formal and better alternatives, for I translate by my knowledge all these names, and it would be really important for BIMC.]]>

They are usually defined or named in terms of balls or objects in boxes or urns. I have never heard of anything else. That page is from Rota, it covers every type of combinatorics problem there is.

]]>You might want to take a look here when you have time.

]]>a. (a1, a2, a3, a4, a5) and (a1, a3, a4, a2, a5) are different solutions. All solutions contains all 5 objects.

b. (a1, a2, a3), (a1, a2, a4), (a1, a3, a2) are different solutions. (a1, a1, a4) is not, for repetition not allowed.

c. (a1, a2, a3) and (a2, a3, a5) are different solutions. (a1, a2, a3) and (a2, a3, a1) are the same. (a1, a3, a3) is not a solution.

I'm afraid I would be away now because it's late. I'll be back GMT 8:00 am. So I look for the answers then.

And I only need the words. I'm sure I know the formulae, just I don't have enough time.]]>

d, A way of choosing AND arranging k objects from S, repetition allowed, order matters.

Choosing k objects from n distinct objects with repetition and order matters is n ^ k

]]>e. The above 2 would be the same solution, as order doesn't matter.]]>