In a city all telephone numbers have six digits. The first two digits are always 41 or 42 or 46 or 62. How many telephone numbers have all six distinct digits?

Explanation

To solve the problem of how many six-digit telephone numbers can be formed in a city where the first two digits are either 41, 42, 46, or 62, and all six digits must be distinct, we can follow these steps:

### Step 1: Identify the total digits available
The total digits available are from 0 to 9, which gives us 10 possible digits.

### Step 2: Determine the first two digits
The first two digits can be one of the following combinations: 41, 42, 46, or 62. This gives us 4 different cases to consider.

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