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.....
DOES ORDER MATTER?
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 ORDER IS CHANGED IS SOMETHING DIFFERENT CREATED?
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
- grouping coins
- connecting dots to make diagonals or triangles