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Find Number of Ways

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nycmathdad

Member
Mar 21, 2021
75
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?
 

jonah

Active member
Feb 21, 2015
105
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.
Look it up laddie.
 

Country Boy

Well-known member
MHB Math Helper
Jan 30, 2018
802
Personally, I would not worry about what it is called! There are 5 dogs any one 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.)
 
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nycmathdad

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Mar 21, 2021
75
Personally, I would not worry about what it is called! There are 5 dogs any one 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?
 

jonah

Active member
Feb 21, 2015
105
...
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?
There you go again asking volunteer helpers to post a war and peace explanation for something that you could just read from your textbook. Read your book. Reading is good for you.