Question

4. (3 pts) A combination lock has a four-digit combination nin^ngn4, where ni,n2, ng, and n4 are integers in {0,1,...,9}. (a) (1 pt) How many lock combinations are possible if each digit can be repeated? (b) (2 pts) If the digits in the combination cannot be repeated, then what is the probability of someone guessing the correct four-digit combination? 3

Answer 1

(a)

If each digit can be repeated:

Number of possible combinations = 10⁴ = 10,000

(b)

If each digit cannot be repeated:

Number of possible combinations = 10 X 9 X 8 X 7 = 5040

So,

Probability of guessing = 1/5040 = 0.0001984

So

Answer is:

0.0001984