A combination lock will open when the right choice of three numbers (from 1 to 35)is selected.How many different lock combinations are possible?
A)1,225
B)42,875
C)128,625
D)35
E)105

Question

Quizplus · Accepted Answer

Since the combination lock requires three numbers chosen from 35, and the order in which these numbers are chosen matters (as each represents a distinct position in the combination), we use permutations. The formula for permutations of n items taken r at a time is nPr = n! / (n-r)!. Here, n = 35 (the numbers to choose from) and r = 3 (the numbers to be chosen). Thus, the number of permutations is 35P3 = 35! / (35-3)! = 35! / 32! = 35 x 34 x 33 = 42,875.

A Combination Lock Will Open When the Right Choice of Three