A combination lock will open when the right choice of three numbers (from 1 to 36) is selected.How many different lock combinations are possible?
A) 139,968
B) 1296
C) 36
D) 108
E) 46,656

Question

Quizplus · Accepted Answer

To find the total number of possible lock combinations, we need to calculate 36 Choose 3 (denoted as C(36,3)) which is equal to:

C(36,3) = (36!)/(3!(36-3)!)

Simplifying this expression, we get:

C(36,3) = (36 x 35 x 34)/(3 x 2 x 1)

C(36,3) = 12 x 35 x 34

C(36,3) = 14, 616

Therefore, the total number of lock combinations possible is 14,616.

A Combination Lock Will Open When the Right Choice of Three