Question

A Store-It-All storage facility requires users to enter a four digit code, using numbers 0-9, to get through the gate. You need to get a box of winter clothes from your storage container, but you forgot the code.

How many possible codes are there if the digits cannot be repeated?

What is the probability that you will guess the correct code on your first try?
P(correct code) = ______

Answer 1

There are 5,040 possible codes for a 4-digit lock using numbers 0-9 without repeating digits. The probability of guessing the correct code on the first try is about 0.0001984.

Step-by-step explanation:

The number of possible codes for a 4-digit lock using the numbers 0-9 without repeating any digit can be calculated using permutations, because the order in which we select the digits matters. The first digit has 10 possible choices (0-9), the second digit then has 9 choices (since one digit has already been used), the third has 8 choices, and the fourth has 7 choices. So, the total number of possible codes is calculated as 10 x 9 x 8 x 7.

The probability of guessing the correct code on the first try is simply the reciprocal of the number of possible codes. Since there's only one correct code, the probability is 1 divided by the total number of possible codes.

Calculation:

• Total Number of Possible Codes = 10 x 9 x 8 x 7 = 5040
• P(correct code) = 1 / Total Number of Possible Codes = 1 / 5040 ≈ 0.0001984