There are 12 runners in a race. In how many ways can the first, second, and third place finishes occur? (Assumethere are no ties.)
A) 1320
B) 220
C) 1324
D) 218

Question

Quizplus · Accepted Answer

This is a permutation problem because the order in which the runners finish matters. The formula for permutations is nPr = n! / (n-r)!, where n is the total number of items (runners) and r is the number of items being chosen (top 3 finishers). Here, n=12 and r=3, so the calculation is 12P3 = 12! / (12-3)! = 12! / 9! = 12 x 11 x 10 = 1320.

There Are 12 Runners in a Race