## Precalculus (6th Edition) Blitzer

The number of ways to select 6 numbers from 59 numbers in the New York State lottery is $45,057,474$
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}