How many possible combinations are there for a seven-digit phone number if the first digit of the phone number must be odd?
To answer this question, we can break down the problem into smaller steps:
Step 1: Determine the number of possible options for the first digit.
Since the first digit of the phone number must be odd, it can only be one of the odd digits: 1, 3, 5, 7, or 9. Therefore, there are 5 possible options for the first digit of the phone number.
Step 2: Determine the number of possible options for each of the remaining six digits.
For each of the remaining six digits of the phone number, there are 10 possible options: the digits 0 through 9.
Step 3: Calculate the total number of combinations.
To find the total number of combinations, we need to multiply the number of options for each digit together. Since each digit has the same number of options (10 options), we can simply raise 10 to the power of 6 (since there are six remaining digits). Mathematically, it would be 10^6, which equals 1,000,000 combinations.
However, we need to account for the restriction that the first digit must be odd. Since there are 5 possible options for the first digit, we can multiply the result by 5 to get the total number of combinations.
Therefore, the total number of possible combinations for a seven-digit phone number with the first digit being odd is 5 * 10^6 = 5,000,000 combinations.