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)45
B)977,407,200
C)6
D)720
E)8,145,060

Question

Quizplus · Accepted Answer

The total number of selections possible is calculated using the combination formula since the order of the numbers selected does not matter. The formula for combinations is C(n, r) = n! / [r!(n - r)!], where n is the total number of items to choose from, r is the number of items to choose, and "!" denotes factorial. Here, n = 45 and r = 6. Therefore, the total number of selections possible is C(45, 6) = 45! / [6!(45 - 6)!] = 8,145,060.

To Win a State Lottery Game, a Player Must Correctly