Final answer:
The probability of randomly choosing the correct combination on a combination lock with 40 numbers is 1 / 59,280, which is closest to 1 / 60,000 when rounded. The nearest provided answer option is 1 / 64,000 (option b), although it is not exactly correct.
Step-by-step explanation:
The student has asked what the probability is of randomly choosing the correct three-number combination on a combination lock that has 40 numbers on its dial. There are 40 possible numbers for the first digit, 39 remaining numbers for the second digit, and 38 remaining numbers for the third digit, since you cannot repeat a digit. This results in a total of 40 x 39 x 38 possible unique combinations.
Since there is only one correct combination, the probability of choosing that combination randomly is 1 divided by the total number of combinations. Therefore, the probability is:
1 / (40 x 39 x 38) = 1 / 59,280 or about 1 / 60,000 after rounding to the nearest ten thousand, which is the closest answer to the options provided.
No answer in the multiple choices exactly matches this calculated probability. However, if the student is required to choose the closest answer, option b (1 / 64,000) would be the nearest choice. Yet, it is essential to point out that the exact probability is 1 / 59,280.