Math Problem

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Old 12-06-2022, 07:22 PM
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A music festival award gives awards for 1st, 2nd and 3rd place in each category. If there are 7 contestants for piano and 9 for violin, in how many different ways could the 6 awards be presented?
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Old 12-06-2022, 07:49 PM
retiredguy123 retiredguy123 is offline
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I don't understand the question. Wouldn't you give the awards to the 3 best contestants in each category? So, I guess my answer would be that there is only one way that is fair and makes sense.
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Old 12-06-2022, 08:04 PM
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There is 1st, 2nd and 3rd place for piano, and 1st, 2nd and 3rd place for violin. Well, the question also assumes that even the worst player could get 1st.
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Old 12-06-2022, 08:16 PM
tuccillo tuccillo is offline
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I believe what you are looking for are the number of permutations. If that is the case, the number is 210 for the first category and 504 for the second category.


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A music festival award gives awards for 1st, 2nd and 3rd place in each category. If there are 7 contestants for piano and 9 for violin, in how many different ways could the 6 awards be presented?
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Old 12-06-2022, 08:26 PM
retiredguy123 retiredguy123 is offline
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LOL. So, the awards are randomly selected? I could solve it, but I have had too many adult beverages.

I think the best player should get first place. Why would you give the worst player an award? Not a math problem. Sounds like woke problem.
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Old 12-06-2022, 08:31 PM
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I took the problem from a school math test. The question is looking for the total possibilities…( and that’s where I made a mistake when I tried it. )
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Old 12-06-2022, 08:34 PM
tuccillo tuccillo is offline
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If you want the number of permutations of 6 winners (when considering only 1-2-3 place within each of the two categories), I believe the number is 105,840.

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I took the problem from a school math test. The question is looking for the total possibilities…( and that’s where I made a mistake when I tried it. )
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Old 12-06-2022, 08:37 PM
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Quote:
Originally Posted by tuccillo View Post
If you want the number of permutations of 6 winners (when considering only 1-2-3 place within a group), I believe the number is 105,840.
Yes! That’s where I made my mistake, I added instead of multiplied.(Standardized grade 7 math test.)
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Old 12-06-2022, 08:38 PM
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(7x6x5)x(9x8x7)

What Tuccillo said.
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Old 12-06-2022, 08:52 PM
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Interesting approach, just divide out the denominator.

For those who are curious, the general formula for permutations is:

n! / (n-s)!

where n is the number of objects you are considering and s is the number of objects in each set. Apply this to each of the two categories and then multiply.



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(7x6x5)x(9x8x7)

What Tuccillo said.
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Old 12-06-2022, 09:48 PM
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First prize can go to any 1 of the 15 participants, So 15 choices.

2nd prize can then go to 1 out of the remaining 14.

And 3rd can go to any one of the remaining 13.

So number of ways we can do this is 15*14*13

3*5*2*7*13

3*10*91

2730 ways.
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Old 12-06-2022, 10:25 PM
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Quote:
Originally Posted by Velvet View Post
A music festival award gives awards for 1st, 2nd and 3rd place in each category. If there are 7 contestants for piano and 9 for violin, in how many different ways could the 6 awards be presented?
For the piano (7 total participants): There are 210 possible arrangements (permutations) of 3 participants. 7 possibilities for 1st Place, 6 possibilities for 2nd place, and 5 possibilities for 3rd place. Multiplying these (7x6x5) gives you 210 possible arrangements.

For the Violin (9 total participants) : There are 504 possible arrangements (permutations) of 3 participants. 9 possibilities for 1st Place, 8 possibilities for 2nd place, and 7 possibilities for 3rd place. Multiplying these (9x8x7) gives you 504 possible arrangements.

So, the total number of ways the trophies can be presented is 7 x 6 x 5 x 9 x 8 x 7 = 105,840.

[ In other words the piano 1st place trophy would be given to one of seven participants; the piano 2nd place trophy would be given to one of the remaining six participants, and the piano 3rd place trophy would be given to one of the remaining 5 participants. Similarly, the violin 1st place trophy would be given to one of nine participants; the violin 2nd place trophy would be given to one of the remaining eight participants; and the violin 3rd place trophy would be given to one of the remaining 7 participants. ]
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Old 12-07-2022, 06:19 AM
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My grandson loves math.
I can't even understand any of the stuff he does.
Kids today are so far in front of where we were at same age.
I was a bit thick anyway, but I knew how to work out my hours and wages!
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Old 12-07-2022, 06:23 AM
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Default Simple Math

It’s a perm, because order does matter. Don’t treat it as a combination.
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Old 12-07-2022, 06:59 AM
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Quote:
Originally Posted by tuccillo View Post
If you want the number of permutations of 6 winners (when considering only 1-2-3 place within each of the two categories), I believe the number is 105,840.
another vote for Tuccillo's answer

As an aside, my maternal grandmother's village in England held an annual Show and one year refused to give a 1st Place for the carrots as none of the entries was considered good enough. They just awarded 2nd and 3rd.
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