Answer
The number of ways to select 6 numbers from 59 numbers in the New York State lottery is $45,057,474$
Work Step by Step
We know that the number of ways in which r number of things are chosen from n number of things is obtained by:
${}_{n}{{C}_{r}}=\frac{n!}{r!\left( n-r \right)!}$
From the information,
$\begin{align}
& n=59 \\
& r=6 \\
\end{align}$
Then, we have to find the number of combinations of 59 things taken 6 at a time:
$\begin{align}
& {}_{59}{{C}_{6}}=\frac{59!}{6!\left( 59-6 \right)!} \\
& =\frac{59!}{6!53!} \\
& =\frac{59\times 58\times 57\times 56\times 55\times 54\times 53!}{\left( 53! \right)\times 6\times 5\times 4\times 3\times 2\times 1} \\
& =45,057,474
\end{align}$
