In a state lottery there are 12 finalists eligible for the Big Money Draw. In how many ways can the first, second, and third prizes be awarded if no ticket holder may win more than one prize?
A) 1,478 different selections
B) 1,320 different selections
C) 2,190 different selections
D) 1,220 different selections
E) 2,240 different selections
F) 1,143 different selections

Question

In a state lottery there are 12 finalists eligible for the Big Money Draw. In how many ways can the first, second, and third prizes be awarded if no ticket holder may win more than one prize? ​
A) 1,478 different selections
B) 1,320 different selections
C) 2,190 different selections
D) 1,220 different selections
E) 2,240 different selections
F) 1,143 different selections

Quizplus · Accepted Answer

This is a permutation problem because the order in which the prizes are awarded matters and no ticket holder can win more than one prize. The formula for permutations is nPr = n! / (n-r)!, where n is the total number of items and r is the number of items to choose. Here, n=12 (finalists) and r=3 (prizes), so the calculation is 12P3 = 12! / (12-3)! = 12! / 9! = 12 x 11 x 10 = 1,320 different selections.

In a State Lottery There Are 12 Finalists Eligible for the Big