How can I tell the difference between a permutation and a combination?

It really depends on the context of the question. Alot of practice should do the trick.

Consider these two situations:
-How many words can be formed with the letters a, b, c and d
-How many 5 card hands can be made from a deck of 52 cards

Now in the first sitation we are talking about "words". Now, from general knowledge, we know that in a word, the order of the letters matter. So the word "abc" is not the same as the word "acb".

In a hand of cards, however, the case is different. A hand consisting of the cards in the order:

5H 6H 7H QD 9S

Is exactly the same as the deck:

6H 5H 7H 9S QD

Even though they are listed differently. The first situation is a permuation, while the second is a combination.

The way i like to think of it is:

"A permutation is an arrangement of objects from a set, while a combination is just a selection of objects from a set"

Permutations and combinations

When we talk of permutations and combinations in everyday talk we often use the two terms interchangeably. In mathematics, however, the two each have very specific meanings, and this distinction often causes problems.

In brief,

The Permutation of a number of objects is the number of different ways they can be ordered; i.e. which is first, second, third, etc. If you wish to choose some objects from a larger number of objects, the way you position the chosen objects is also important.

With Combinations, on the other hand, one does not consider the order in which objects were chosen or placed, just which objects were chosen.

We could summarise permutations and combinations (very simplistically) as

P-ermutations - p-osition important (although choice may also be important)

C-ombinations - c-hosen important,
which may help you to remember which is which.

I'm also shaky upon which word to use to represent an ordered list or the whole group. No matter how hard I've tried, the correct term doesn't stick. I don't have any neat aide-memoire to offer though I can say that I have no difficulty remembering which formula I need. The key question being Is order important? Would changing the order change the solution to an unacceptable one.

The reason I have trouble with the terms Combination and Permutation is that I rarely use permutation in normal conversation yet I do use combination locks almost daily. Unfortunately the number of codes on a combination lock isn't a combination at all! Pity we didn't call them Permutation locks .