Math CentralQuandaries & Queries


Question from Marcy, a teacher:

I'm having difficulty teaching my students when to use permutations or combinations. Is there a "catchy" way to teach them that will help them to identify when to use permutations and combinations?

Hi Marcy,

The problems are so varied that it impossible to give a simple rule that will tell you when to use permutations and when to use combinations. The one question to ask yourself when approaching a problem is "Does order matter?" If the answer is yes then you probably need to use a permutation.

For example if there are 24 students in your class and you are going to select 2 of them to perform two small tasks for you then there are 24 choose 2 ways to select the two students. There is no order involved so this is a combination. If however you are going to select one student to take a message to the principal's office and another to bring you something from the storage room then you can select the two students for these tasks in 24 × 23 ways. This is a permutation since order is involved. The first selected student will go to the principal's office and the second student will go to the storage room.

I hope this helps,

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