A certain lock has four tumblers, and each tumbler can assume three positions. How many different possibilities are there?
3^4=81
To determine the number of different possibilities for a lock with four tumblers, with each tumbler having three positions, we can use the concept of permutations.
Since each tumbler can assume three positions, there are three choices for the first tumbler, three choices for the second tumbler, three choices for the third tumbler, and three choices for the fourth tumbler.
To determine the total number of possibilities, we multiply the number of choices for each tumbler: 3 * 3 * 3 * 3 = 81.
Therefore, there are 81 different possibilities for a lock with four tumblers, each having three positions.