Question

Part A: A keypad lock asks you to input a four-digit code. If you can choose any digit, 0 through 9, for each of the four digits, how many possible combinations are there? Part B: Suppose the similar keypad lock asks for a four-digit code but does not allow you to repeat a digit. How many possible combinations are there for this lock?

Answer 1

A. 10,000 combinations

B. 5,040 combinations

Explanation:

A. four-digit code from 0-9 without restriction

1st digit - 10 options

2nd digit - 10 options

3rd digit - 10 options

4th digit - 10 options

Number of possible options = 10 * 10 * 10 * 10 = 10^4 = 10,000 combinations

b. No repetition of digits

1st digit = 10 options

2nd digit = 9 options

3rd digit = 8 options

4th digit = 7 options

Number of possible choices = 10 * 9 * 8 * 7 = 5,040 combinations