Answer
To select 6 numbers out of 53 numbers for the LOTTO in the state of Florida, there are a total of $22,957,480$ possibilities.
Work Step by Step
We know that:
${}_{n}{{C}_{r}}=\frac{n!}{r!\left( n-r \right)!}$
So, from the information,
$\begin{align}
& n=53 \\
& r=6 \\
\end{align}$
Then, we have to find the number of combinations of 53 things taken 6 at a time:
$\begin{align}
& {}_{53}{{C}_{6}}=\frac{53!}{6!\left( 53-6 \right)!} \\
& =\frac{53!}{6!47!} \\
& =\frac{53\times 52\times 51\times 50\times 49\times 48\times 47!}{\left( 47! \right)\times 6\times 5\times 4\times 3\times 2\times 1} \\
& =22,957,480
\end{align}$
