How Many Possible Outcomes for 10 Cricket Matches with Three Win Options Each?

AI Thread Summary
The discussion centers on calculating the total possible outcomes for 10 cricket matches, each with three potential results: a win for the first team, a draw, or a win for the second team. The original poster mistakenly applies the combinations formula, suggesting that 10 choose 3 yields 120 combinations. However, the correct approach involves recognizing that each match's outcome is independent, leading to a total of 3^10 possible outcomes, which equals 59,049. The conversation emphasizes the importance of understanding independent events in probability rather than using combinations. Ultimately, the correct calculation reveals the vast number of potential outcomes for the matches.
rama1001
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Homework Statement



There are 10 cricket matches are on to start and each match can result three types of wins i.e. either first team win or draw or second team win. How many combinations can possible to make all the cricket matches should be right, if a user select only one option per match(i.e first team win or draw or second team win) over all the 10 matches?

Homework Equations



No Hints at all.

The Attempt at a Solution



I guess that combinations concept is quite suitable for this operation but i am not sure. if i take the formula N combinations r i.e. 10combinations3 which results 120 combinations. Am i right?

Any help here!
 
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Shouldn't the 10 cricket matches beconsider as unique cricket matches?
 
no every match is different allways.
 
rama1001 said:

Homework Statement



There are 10 cricket matches are on to start and each match can result three types of wins i.e. either first team win or draw or second team win. How many combinations can possible to make all the cricket matches should be right, if a user select only one option per match(i.e first team win or draw or second team win) over all the 10 matches?

Homework Equations



No Hints at all.

The Attempt at a Solution



I guess that combinations concept is quite suitable for this operation but i am not sure. if i take the formula N combinations r i.e. 10combinations3 which results 120 combinations. Am i right?

Any help here!

If you are saying that all 10 choices must be right, combinations have nothing at all to do with the problem. Can't you see why?

I will give you a small hint. Suppose we bet on 2 matches instead of 10. What is the probability we get both bets right? Well, what is the probability the first guess is right? What is the probability the second guess is right? Assuming independence of outcomes, what is the probability that both guesses are right?

Now extend the reasoning to 10 guesses.

RGV
 

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