Out of 36 random drawings what are the odds of numbers 1-12 each coming up 3 times?

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whoisthewomanme

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If you had 12 possible outcomes what are the odds that each outcome would come up exactly 3 times out of 36 drawings?
So I'm going to make a random drawing 36 times and the outcome can be numbers 1-12. What are the odds, that each number would come out exactly 3 times?


(the numbers are not removed after having coming up, they are still included in future drawings)
 
whoisthewomanme said:
If you had 12 possible outcomes what are the odds that each outcome would come up exactly 3 times out of 36 drawings?
So I'm going to make a random drawing 36 times and the outcome can be numbers 1-12. What are the odds, that each number would come out exactly 3 times?


(the numbers are not removed after having coming up, they are still included in future drawings)
Click to expand...

What are your thoughts?

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You need to read the rules of this forum. Please read the post titled "Read before Posting" at the following URL:

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I'm aware that the probability is:

36! / (3!)^12
____________
12^36


However, I'm not sure how to convert this into a percentage. Obviously, reduce the fraction, and multiply that with 100%.

However, I'm having trouble reducing the fraction since the numbers are so large.
 
whoisthewomanme said:
i'm aware that the probability is:

36! / (3!)^12
____________
12^36


however, i'm not sure how to convert this into a percentage. Obviously, reduce the fraction, and multiply that with 100%.

However, i'm having trouble reducing the fraction since the numbers are so large.
Click to expand...

36! / (3!)^12
____________ ~ 2.41099e-07 = 0.0000241099%
12^36

I would have thought that modern calculators would do this easily. The largest individual expression [36!] is only about 1041


EDIT: Fix dumb mistake - but it was the program, it wasn't me:oops:
 
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whoisthewomanme said:
I'm aware that the probability is:

36! / (3!)^12
____________
12^36


However, I'm not sure how to convert this into a percentage. Obviously, reduce the fraction, and multiply that with 100%.

However, I'm having trouble reducing the fraction since the numbers are so large.
Click to expand...

Since you are interested in % - and there are no subtraction of near equal numbers are not involved - exact numbers do not matter

36! = 3.71993E+41

12^36 = 7.08802E+38

6^12 = 2176782336


Now go at it!!!
 
Thanks everyone. This is pretty clear now.

I came up with 0.00241099 also.

Perhaps Denis' 0.0000241099 is correct though?

I plan on multiplying this event (36 drawings = 1 event) by like 1,000,000 events.

Big difference between the two.

The first is 0.00241099 x 1,000,000 = 2410.99 (converted to percentage it would 24.1099% correct?)

The second number that Denis came up with would be 0.0000241099 x 1,000,000 = 24.1099 (converted to percentage it would be 0.241099% correct?)

Thanks again everyone!
 
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whoisthewomanme said:
Thanks everyone. I now understand what I was doing incorrectly.
Click to expand...
What was the error? (This is why posters are asked to show their work.)

whoisthewomanme said:
I came up with 0.00241099% also.

Perhaps Denis' 0.0000241099 is correct though?
Click to expand...
Um... 0.000 024 is the exact same thing as 0.002 4%. Did they not cover percentages and decimals in your classes?

whoisthewomanme said:
I'm aware that the probability is:

. . . . .\(\displaystyle \dfrac{\left(\dfrac{36!}{(3!)^{12}}\right)}{12^{36}}\)
Click to expand...
Are you "aware" because they gave you that expression here? :shock:
 
stapel said:
What was the error? (This is why posters are asked to show their work.)


Um... 0.000 024 is the exact same thing as 0.002 4%. Did they not cover percentages and decimals in your classes?


Are you "aware" because they gave you that expression here? :shock:
Click to expand...


The error was me trying to program it on a Ti-83+. lol

Should have just used Google as the others did.

And I've been out of school for quite a long time. My sister is taking a college course on probability and statistics and she asked me if I could help out with this one.

Yes, I was the one asking at your link. Quickly started remembering a lot of these things from my school days but not everything entirely.
 
Denis said:
100/100 ?

Anyway, that was my "percentage" result: was questioning Ishuda...

36! / 6^12 / 12^36 = .000000241

.000000241 * 100 = .0000241 % : PERCENTUM!!
Click to expand...
I think you should look again -that's what I said:oops:
 
Denis said:
This is what I was questioning:
36! / (3!)^12
____________ ~ 2.41099e-05 = 0.00241099%
12^36

But you edited it AFTER...

Anyway, this thread is getting ridiculous...I quit :idea:
Click to expand...

Yes and all the edits were there for everyone to see along with the "oops"
 
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