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Question

# Use the formula for$_nC_r$to solve. To win in the New York State lottery , one must correctly select 6 numbers from 59 numbers. The order in which the selection is made does not matter. How many different selections are possible?

Solution

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In order to solve this equation, we need to use the formula for the number of combinations, $_nC_r$ of $n$ things taken $r$ at a time.

$_nC_r=\dfrac{n!}{(n-r)!r!}$

Based on the problem, we have $n=59$ which represents the total possible lotto numbers and $r=6$ which represents the number of lotto numbers taken.

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