Explain How You got the answer please, because the answer I keep getting doesn't even match any of the answers.
A telephone dial has holes numbered from 0 to 9 inclusive, and eight of these holes are also lettered. How many different telephone numbers are possible with this dial, if each "number" consists of two letters followed by five numbers, where the first number is not zero?
200,000
5,760,000
6,400,000
To determine the number of possible telephone numbers, we need to count the number of choices available for each position in the number.
To calculate the number of choices for each position, we can break down the problem into individual components:
1. First Letter: There are 8 holes with letter labels on the dial. So, there are 8 choices for the first letter.
2. Second Letter: Since we can repeat letters, there are also 8 choices for the second letter.
3. First Number: There are 9 holes (excluding 0) for the first number. So, there are 9 choices.
4. Second Number: There are 10 holes (0 to 9) for the second number. Hence, 10 choices.
5. Third Number: Similarly, there are 10 choices for the third number.
6. Fourth Number: Again, 10 choices.
7. Fifth Number: Once more, 10 choices.
To find the total number of possibilities, we need to multiply the number of choices for each position:
8 choices × 8 choices × 9 choices × 10 choices × 10 choices × 10 choices = 4,608,000
Therefore, the correct answer is 4,608,000.