Perms and Combs Got You Down

How can you tell if you are dealing with a Perm situation or a Comb situation?

The Perms and Combs unit in math 30-1, and -2 is primarily about one thing.



The question is, "given a dozen donuts in a box, how many ways can you grab two of them?"

There are two types of counting that you can consider using, Permutations or Combinations.


Knowing which type of counting to use can be one of the trickiest questions in this unit. Most students learn how to do permutations in the permutations section of their books, and learn how to do combinations in the combinations section. 

Unfortunately tests do not come in sections.

Therefore students are taught to ask.....



if yes-------> use permutations

if no--------> use combinations


This question yields the correct answer around 30% of the time. It is used because it is short and snappy and therefore easy to remember.


The more effective question to ask is.....



if yes -----> use permutations

if no ------> use combinations

This question correctly indicates which to use around 80% of the time.


Here are a few examples:

if I change the order or the letters in NOW to WON do I get something different?

yes, therefore perms would be used here ( or the FUndamental Counting Principle)


If You are in line to buy the new iPHONE and someone changes the order by butting in front of you do you having something different?

yes, therefore perms would be used here


If you are playing poker and you are dealt 10, Jack, Queen, King, and Ace and you decide to change the order that you are holding the cards do you now have something different

no, therefore combs would be used

(if you think the above should be yes call me, I will get you into our Saturday night game)


Overall, you can start cataloging which situations use perms and which situations use combs.



  • letter rearranging
  • # rearranging
  • committees in which different people have different jobs
  • line ups
  • committees in which all members are equal 
  • cards
  • grouping coins
  • connecting dots to make diagonals or triangles

Combine this cataloging with the use of the correct question to ask yourself and you will likely decide correctly 99 times out of 100 whether to use perms or to use combs.

Stay tuned to this blog  for more helpful tips on some important types of questions from the Perms and Combs unit, like what to do about creating even #'s when there is a zero in the #s you can choose from.

P.S. Anybody know whether Perms or Combs would be used in the donut example above?




Dec 10, 2012 Posted by: Tom MacFarlane
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