# Find Number of Ways

• MHB
At a recent dog show, there were 5 finalists. One of the finalists was awarded "Best in Show" and another finalist was awarded "Honorable Mention." In how many different ways could the two awards be given out?

The words "how many ways" reminds of probability. I just don't recall if this is a combination or a permutation.

I will take a guess and say this is a combination problem.

The set up is 5C2.

You say?

jonah1
Beer soaked ramblings follow.
At a ...
I will take a guess and say this is a combination problem.

The set up is 5C2.

You say?
I say stop guessing.
You have a textbook.

HOI
Personally, I would not worry about what it is called! There are 5 dogs anyone of which could be declared "best in show". Once that had been chosen, there are 4 dogs left that could be chosen "honorable mention".

There are a total of 5(4)= 20 ways that could be done.

(Since order, which dog is "best in show" and which is "honorable mention", is relevant, this is a "permutation" problem but, as I say, that is really not important.)

Personally, I would not worry about what it is called! There are 5 dogs anyone of which could be declared "best in show". Once that had been chosen, there are 4 dogs left that could be chosen "honorable mention".

There are a total of 5(4)= 20 ways that could be done.

(Since order, which dog is "best in show" and which is "honorable mention", is relevant, this is a "permutation" problem but, as I say, that is really not important.)

Are you saying that that 5C2 should be 5P2?

Let me see.

5P2 = 5!/(5 - 2)!

5P2 = 120/(3)!

5P2 = 120/6

5P2 = 20 ways.

When it comes to combination versus permutation, in terms of combination order does matter. Order does not matter in terms of permutation. Can you explain why that is the case using a simple math example for both cases?

jonah1
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When it comes to combination versus permutation, in terms of combination order does matter. Order does not matter in terms of permutation. Can you explain why that is the case using a simple math example for both cases?