Probability and Combinations

In summary, the problem is asking for the number of possible combinations if a user selects one option per match for 10 cricket matches, with each match having three possible outcomes (first team win, draw, or second team win). The formula for combinations does not apply in this case as all 10 choices must be correct. Instead, the probability of getting all 10 choices correct can be calculated by multiplying the probabilities of each individual choice being correct, assuming independence of outcomes."
  • #1
rama1001
132
1

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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  • #2
Shouldn't the 10 cricket matches beconsider as unique cricket matches?
 
  • #3
no every match is different allways.
 
  • #4
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
 

What is the difference between probability and combinations?

Probability is the likelihood or chance that a specific event will occur, while combinations refer to the different ways in which a set of items can be arranged or selected. Probability involves calculating the likelihood of a specific outcome, while combinations involve counting the number of possible outcomes.

How do you calculate the probability of an event?

To calculate the probability of an event, you divide the number of favorable outcomes by the total number of possible outcomes. This will give you a decimal, which can then be converted to a percentage by multiplying by 100.

What is the difference between permutations and combinations?

Permutations refer to the different ways in which a set of items can be arranged in a specific order, while combinations refer to the different ways in which a set of items can be selected without regard to order. Permutations involve all items in the set, while combinations do not necessarily include all items.

How do you calculate the number of combinations?

To calculate the number of combinations, you use the formula nCr = n! / (r! * (n-r)!), where n represents the total number of items and r represents the number of items being selected. This formula can also be written as nCr = nPr / r!, where nPr represents the number of permutations.

What real-world applications use probability and combinations?

Probability and combinations are used in many fields, such as finance, statistics, and science. Some real-world applications include predicting stock market trends, conducting medical experiments, and analyzing sports statistics. They are also used in everyday situations, such as calculating the odds of winning a game of chance or choosing a lottery ticket.

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