## Precalculus (6th Edition) Blitzer

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.
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}