Is it likely to win the Euromilhões?

In order to calculate this probability, we have to firstly know the amount of different bets that are possible to make in a “Euromilhões” form. First of all it is worth to have in mind that there is no repetition and so it is not possible to choose the same number twice. The order is not relevant, this is, it is indifferent to first choose 8 and than 9 or the contrary. Therefore we are in the presence of combinations. We can bet 5 numbers among 50 and 2 stars among 11. The formula to calculate the possible amount of combinations is the following: `text()^50 C_5 xx text()^11 C2 = 116.531.800`.

Can I take all the possible bets and win?

There are 116.531.800 possible cases to bet in the “Euromilhões”. If we want to be completely sure we will win, we have to bet all the combinations. Having in mind that we have to pay 2€ for each bet, we would have to spend 233.063.600€. Even if the first prize was 180 million Euros, it would not be worth. Even if we think about the second, the third or the fourth prize, it is hardly worth (besides that, would need the initial money). Besides that, there is no guarantee that in that same week there is not another winner and so we would have to share the Jackpot with him/her!

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