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How many possibilities are there for Lotto 6 out of 49?

Info by Square | 13/04/2012 at 22:48

Often, in math class, it comes to the question of how many possible combinations are there actually in lotto 6 out of 49. Also lottery players should be aware before they senseless waste their money.

First of all, let's have a look at the calculation:

\[{49\choose 6} = \frac{49!}{(49-6)!*6!} = \frac{49!}{43! * 6!}= 13.983.816\]

In the case of the lottery numbers (sampling without putting back with 49 options and 6 times pulling), we get to the result by calculating 49 above 6. The probability in percentage, we can calculate as follows:

\[\frac{1}{13.983.816}*100=0,00000715\]

So, there are a total of 13,983,816 different possibilities for the outcome of the lottery. This means, that on average, only one from 14 million tips wins and the probability of 6 correct numbers is only 0.00000715 percent!

But with the many millions of tips that are issued at each lottery drawing, it is only likely that from time to time someone wins. But whoever it is, is pure luck.

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