To win a state lottery game, a player must correctly select six numbers from the numbers 1 through 49. Find the total number of selections possible if a player selects only even numbers.
A)144
B)96,909,120
C)6,991,908
D)134,596
E)60,410,085,120

Question

Quizplus · Accepted Answer

There are 24 even numbers between 1 and 49 (inclusive). The total number of ways to select 6 numbers out of these 24 is calculated using combinations (since the order of selection does not matter), which is given by the formula $C(n, r) = \frac{n!}{r!(n-r)!}$, 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 $n$. Therefore, the total number of selections possible is $C(24, 6) = \frac{24!}{6!(24-6)!} = \frac{24!}{6!18!} = 134,596$.

To Win a State Lottery Game, a Player Must Correctly