Guaranteed 37611

Determine how many different ways a Lotto ticket can be written if we guess six numbers out of 49. At what Jackpot would it already pay to bet so many tickets to be guaranteed to win the 1st prize? The price of one type is €1.

Correct answer:

n =  13983816 Eur

Step-by-step explanation:

$$\begin{gathered} C_6(49)=\left(\genfrac{}{}{0ex}{}{49}{6}\right)=\frac{49!}{6!(49-6)!}=\frac{49\cdot 48\cdot 47\cdot 46\cdot 45\cdot 44}{6\cdot 5\cdot 4\cdot 3\cdot 2\cdot 1}=13983816 \\ n=\left(\genfrac{}{}{0ex}{}{49}{6}\right)=13983816=13983816\text{Eur} \end{gathered}$$

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