A small combination lock on a suitcase has 4 wheels, each labeled with the 10 digits from 0 to 9 . If an opening combination is a particular sequence of 4 digits with no repeats, what is the probability of a person guessing the right combination?
The probability of a person guessing the right combination is (Type a fraction. Simplify your answer.)
Final Answer: The probability of a person guessing the right combination is \(\boxed{0.0001984126984126984}\).
Step 1 :A small combination lock on a suitcase has 4 wheels, each labeled with the 10 digits from 0 to 9. If an opening combination is a particular sequence of 4 digits with no repeats, we are asked to find the probability of a person guessing the right combination.
Step 2 :The total number of possible combinations is \(10*10*10*10 = 10000\) since there are 10 digits (0-9) and 4 wheels.
Step 3 :However, since the problem states that there are no repeats in the combination, the number of possible combinations is \(10*9*8*7 = 5040\).
Step 4 :The probability of guessing the right combination is therefore 1 out of 5040.
Step 5 :Initially, the probability was calculated as 0.504, which is incorrect. The probability should be 1 divided by the number of valid combinations, not the number of valid combinations divided by the total number of combinations.
Step 6 :Correcting the calculation, the probability is \(\frac{1}{5040} = 0.0001984126984126984\).
Step 7 :Final Answer: The probability of a person guessing the right combination is \(\boxed{0.0001984126984126984}\).