Permutations or Combinations?

Date: 01/09/2003 at 14:44:35
From: Aniela
Subject: Finite math

When given a permutation or combination problem, is there anything 
SPECIFIC to look for to know whether it is one or the other? For 
example, are there any "key words" to look for? 

This also relates to probability. How does one know when to use 
permutations or combinations?

Date: 01/10/2003 at 11:17:05
From: Doctor Ian
Subject: Re: Finite math

Hi Aniela,

This is a good question, but I don't think it has the answer you were
hoping for.  

English is a pretty slippery language, so as a rule, trying to use
little formulas ("When I see the word _____, they must be talking
about _____ instead of _____") is a bad idea.  

The only reliable way to know whether a problem is asking for
permutations or combinations is to write down a few examples of what's
being asked for (e.g., how many ways can you make double-dip cones
from a specified number of ice-cream flavors), and then try to
establish whether or not order makes a difference.  

Sometimes that isn't even something that you can tell by looking at
the words in the problem. Often you just have to use common sense. 
For example, if you're asked to make up committees from a collection
of prospective members, it obviously doesn't matter how you order the
members. But there aren't any special words that will tip you off to
that fact. 

Note that sometimes you need to find permutations OF combinations, or
combinations OF permutations:

   Fast Food Combinations - Dr. Math FAQ
   http://mathforum.org/dr.math/faq/faq.mcdonalds.html 

This is another reason that trying to use keywords to decide what to
do isn't such a great idea. 

I hope this helps.  Write back if you'd like to talk more
about this, or anything else.

- Doctor Ian, The Math Forum
  http://mathforum.org/dr.math/