There are two possibilities for the first three digits, and there are 4! = 24 ways to arrange the remaining four digits.
Therefore, there are a total of 2 * 24 = 48 possible numbers that Megan could dial.
Only one of these numbers is Fatima's correct number.
So the probability that Megan dials Fatima's correct number is 1/48.
The answer is: \frac{1}{48}
Below is a math problem. Provide a detailed, step-by-step solution.

### Problem:
Megan has lost Fatima's phone number. Megan knows that the first three digits are either 296 or 299. The remaining four digits are 0, 1, 6 and 7, but she isn't sure of the order of these digits. If Megan randomly dials a seven-digit number that meets these conditions, what is the probability that she dials Fatima's correct number? Express your answer as a common fraction.

### Answer:
