Final answer:
To calculate the number of 3 by 3 lock combination possibilities, simply multiply the number of options for each of the three positions (10 x 10 x 10), resulting in 1000 different combinations.
Step-by-step explanation:
To calculate the number of 3 by 3 lock combination possibilities, you must consider how many options there are for each position in the combination. Assuming that each position of the lock can be set to any number from 0 to 9 (which is common with combination locks), there would be 10 possible numbers for each of the three positions. To find the total number of combinations, you would multiply the number of choices for each position:
10 (first position) x 10 (second position) x 10 (third position) = 103 = 1000 different combinations.
This is a classic example of the counting principle in combinatorics, the branch of mathematics dedicated to counting combinations and permutations systematically. No shuffling or factorial calculations are needed in this scenario as opposed to calculating combinations of items where order matters.