How do you tell whether the problem is a permutation or a combination???
My name is Ashleigh and I'm in 10th grade in algebra 2.

Hi Ashleigh,

This is certianly a hard thing to learn the first time you see these words and ideas.

The basic distinction is: does the ORDER matter?

In a typical lock on your locker the ORDER you dial the digits matters. In spite of the name you may hear, it is a PERMUTATION.

33-26-7 is different than 7-26-33.

When you play a game of cards, with a 'hand of cards' you pick up the collection and change the order to suit what you are going to do next. The 'deal' of the cards has an order - but by the time you play, it is a COMBINATION - the order your received the cards does not matter.

Usually, when I do these problems, I DO imagine the events happening in a particular order and count those ordered events - the permutations. Typically a count like 8x7x6x5 or nx(n-1)x(n-2) ....

THEN I ask a critical question. Do two of these ordered events come out 'the same'? If yes, then I take my initial collection and say - how many are the same? Maybe with the events above - four things happening - I find that there are 4x3x2x1 different orders which come from the same unordered (or reordered) collection.

Then a basic principle of 'counting' says that you DIVIDE: number of ordered ways to create the set / number of orders which are the same. The fancy mathematical word for 'the same' is "are equivalent".

So combinations are orordered (or something you can reorder so that things look the same). Permutations are a larger number (no division) of things where ANY change in order makes them different.

If you go on to study more of these things, in a field called combinatorics, you will find many variations of order, no order, repetition, no repetition etc. In the end you do NOT memorize a list of formulas and hope for the best. You understand a few basic principles, imagine the events happening, and compare which are the same and which are different in this particular situation. It does become quite fun in the end - but it sure is confusing at the start.

Walter Whiteley

Go to Math Central