Final answer:
The number of different combinations on a three cylinder combination lock with 70 numbers on each cylinder is calculated by taking the product of the number of choices for each cylinder, resulting in a total of 343,000 combinations.
Step-by-step explanation:
The question requires the calculation of the number of different combinations possible on a three cylinder combination lock with 70 numbers on each cylinder. To find the total number of combinations, one must consider that each cylinder can be set to one of 70 positions independently of the others. Since there are three cylinders, the calculation will be 70 × 70 × 70, which is 70 to the power of 3 or 703.
This results in 343,000 possible combinations, because:
This sort of problem is a classic exercise in fundamental combinatorics, which is a branch of mathematics that deals with counting, both as an end in itself and as a way to calculate probabilities. In this instance, the exercise illustrates the basic principle of the counting rule of product, where the total number of outcomes is determined by multiplying the number of choices for each independent event.