A combination lock on a suitcase has 3 wheels, each labelled with nine digits from 1 to 9. If an opening combination is a particular sequence of three digits with no repeats, what is the probability of a person guessing the right combination ?

Explanation

To solve the problem of finding the probability of guessing the right combination for a suitcase lock with 3 wheels, each labelled with digits from 1 to 9, we can follow these steps:

### Step 1: Determine the total number of possible combinations.
Since the combination consists of 3 digits with no repeats, we can calculate the total number of combinations as follows:

1. For the first digit, we have 9 options (1 to 9).
2. For the second digit, since we cannot repeat the first digit, we have 8 options left.
3. For the third digit, we cannot repeat the first two digits, leaving us with 7 options.

Thus, the total number of possible combinations can be calculated by multiplying the number of choices for each digit:

\[ \text{Total Combinations} = 9 \times 8 \times 7 \]

### Step 2: Calculate the total combinations.
Now, let's perform the calculation:

\[ 9 \times 8 = 72 \]
\[ 72 \times 7 = 504 \]

So, the total number of possible combinations is 504.

### Step 3: Determine the probability of guessing the correct combination.
The probability of guessing the correct combination is given by the ratio of the number of successful outcomes (which is 1, since there is only one correct combination) to the total number of possible outcomes (which we calculated to be 504).

\[ \text{Probability} = \frac{\text{Number of Successful Outcomes}}{\text{Total Combinations}} = \frac{1}{504} \]

### Final Answer:
The probability of a person guessing the right combination is:

\[ \frac{1}{504} \]

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