Calculating Lotto 6/49 Odds | Formula Explained

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SUMMARY

The odds of winning the Lotto 6/49 by selecting 6 different numbers from a pool of 49 are calculated using the combination formula 49C6, which is expressed as 49!/(6!*43!). This results in a probability of approximately 1 in 14,000,000. The initial misunderstanding stemmed from treating the selection as a permutation rather than a combination, leading to an inflated figure of 10,068,347,520. Understanding the distinction between combinations and permutations is crucial for accurate probability calculations.

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i was trying to calculate the odds of winning the lotto 6/49 6 diffrent numbers and the numbers go from 1 - 49 could anyone calculate it and show me the formula i thought it would be 49*48*47...*43 but that does not seem right
thanks
 
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whatdofisheat said:
i was trying to calculate the odds of winning the lotto 6/49 6 diffrent numbers and the numbers go from 1 - 49 could anyone calculate it and show me the formula i thought it would be 49*48*47...*43 but that does not seem right
thanks
The probability of choosing the winning number would be 1 out of the number of ordered 6-character strings you can create from a 49 character set without replacement. The latter number is what you calculated, 49 choices for the first character multiplied by 48 choices for the second character, and so on for 6 factors.
 
yes but sequencially multplying thes numbers together gives me 10068347520 which is alittle hey because people usually win the lotto every week and I am sure not that many tickets are sold
 
49C6

Or using the definition of the combination...

49!/(6!*43!)

It's about 1 in 14,000,000, the number you've been hearing in the news for the past week.
 
It does not matter in what order you receive your six numbers, so it is a combination, which is the permutation divided by 6!
 

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