Question

a bicycle lock has a four - digit code. the possible digits, 0 through 9, cannot be repeated. what is the probability that the lock code will begin with the number 5? is the probability that the lock code will not in the number 0? 0.1 0.4 0.5 0.6

Explanation:

Step1: Calculate total permutations

Total digits (0 - 9) = 10. For a 4 - digit code with no repetition, total permutations \( P(10,4)=\frac{10!}{(10 - 4)!}=10\times9\times8\times7 = 5040 \).

Step2: Calculate favorable permutations (begin with 5)

If first digit is 5, remaining 3 digits are chosen from 9 remaining digits. Permutations \( P(9,3)=\frac{9!}{(9 - 3)!}=9\times8\times7 = 504 \).

Step3: Calculate probability

Probability \(=\frac{\text{Favorable}}{\text{Total}}=\frac{504}{5040}=0.1\).

Answer:

0.1