To win a state lottery game, a player must correctly select six numbers from the numbers 1 through 45. Find the total number of selections possible.
A)720
B)8,145,060
C)45
D)977,407,200
E)6

Question

Quizplus · Accepted Answer

The total number of selections possible is calculated using the combination formula, which is $C(n, r) = \frac{n!}{r!(n-r)!}$, where $n$ is the total number of items to choose from, $r$ is the number of items to choose, and $n!$ denotes the factorial of $n$. For this lottery game, $n = 45$ and $r = 6$, so the calculation is $C(45, 6) = \frac{45!}{6!(45-6)!}$, which simplifies to $\frac{45!}{6!39!}$. This calculation results in 8,145,060 possible selections.

To Win a State Lottery Game, a Player Must Correctly