SOLUTION: Hi. I often want to calculate stuff like the example listed below, but am not sure how to do it. I don�t want to bother others with that, would love to learn how to do it proper

Question 626355: Hi.
I often want to calculate stuff like the example listed below, but am not sure how to do it. I don�t want to bother others with that, would love to learn how to do it properly myself. Can you please help me out?
6 competitions are being played.
In each of them there are 32 teams (a total of 192 teams).
What are the chances (probability) of someone predicting all champions correctly (if we assume there are no favourites nor underdogs, all teams are of exactly the same strength on paper).
Cup A � 32 teams
Cup B � 32 teams
Cup C � 32 teams
Cup D � 32 teams
Cup E � 32 teams
Cup F � 32 teams
I�m interested in the probability of guessing all six champions, also (if it�s not too much work to calculate), what is the probability of guessing 5/6, 4/6 and 3/6.
I am not using this for any real-life betting, it�s just for an online management game with no money involved. :) Thanks!!

Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
In each of them there are 32 teams (a total of 192 teams).
What are the chances (probability) of someone predicting all champions correctly (if we assume there are no favourites nor underdogs, all teams are of exactly the same strength on paper).
Cup A � 32 teams
Cup B � 32 teams
Cup C � 32 teams
Cup D � 32 teams
Cup E � 32 teams
Cup F � 32 teams
I�m interested in the probability of guessing all six champions, also (if it�s not too much work to calculate), what is the probability of guessing 5/6, 4/6 and 3/6.
-----
Probability a team takes the Cup: 1/32
---
Probability you choose 6 Cup takers: (1/32)^6 = 9.31x10^-10.
That means 0.000000000931
---------------
Probability you choose 5 winners: 6C5(1/32)^5*(31/32) = 1.73x10^-7
That means 0.000000173
-----
Pick 4: 6C4(1/32)^4(31/32)^2 = 0.0000134
-----
Pick 3: 6C3(1/32)^3(31/32)^3 = 0.000555
==============================================
Cheers,
Stan H.
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