Chapter 10.8, Problem 24STP

To determine

To calculate: The total number of the bicycle lock combinations possible.

Answer to Problem 24STP

The correct answer is Option (J) 10000.

Explanation of Solution

Given: A bicycle lock has 4 rotating discs each containing digits 0 to 9.

Concepts Used: Consider n blank spaces that can be filled with any one of the digits from 0-9 with repetition. Then for the first blank space, any one of the 10 digits can be used to fill the blank. So total possible outcomes for the first blank space is 10. The same theory can be used for all the remaining blank spaces. Thus, using fundamental counting principle, total number of possible outcomes for filling n blank spaces will be

= $10\times 10\times 10\times$ … (n times)

Calculation: The bicycle lock has 4 rotating discs each containing digits 0-9. The first digit of the lock combination can be any one of these 10 digits. So total number of possible outcomes for the first digit of the lock combination is 10. Similarly, since digits can repeat in the combination, the second digit can also be any one of these 10 digits. Same goes for the third and fourth digit of the lock combination. Hence, using fundamental counting principle, total number of possible outcomes for the lock combinations

= $10\times 10\times 10\times 10$

= 10000

The correct answer is given by option (J) 10,000.