Question

A certain 5-digit combination lock can be reset with a new combination. The lock uses numbers from 1 to 6. After a friend accidentally resets it to an unknown combination, what is the probability that you guess the combination that opens the lock? A. 100,000 B. 7,776 C. 1100,000 D. 17,776

Answer 1

The probability of guessing a 5-digit combination lock using numbers from 1 to 6 is 1 out of 7,776 since there are 6^5 possible combinations.

Step-by-step explanation:

The probability of guessing the unknown combination of a 5-digit lock that uses numbers from 1 to 6 is determined by calculating the number of different combinations that can be made with those digits. Since the lock can use the same number more than once (with replacement), for each digit in the combination there are 6 possibilities. Therefore, for all 5 digits, we calculate the total number of combinations by raising the number of possibilities for a single digit to the power of the number of digits in the combination, which is 6^5 or 7,776 combinations.

Each of these combinations is equally likely, so the probability of guessing the correct combination on one try is 1 out of 7,776. The correct answer to the question posed by the student is B - 7,776.