How many seven-digit numbers are there when 0 and 1 cannot be the leading number?
To find the number of seven-digit numbers where 0 and 1 cannot be the leading number, we need to consider two scenarios:
1. When the leading digit is 2-9:
For the leading digit, we can choose any number from 2 to 9, giving us 8 choices. For each of the remaining six digits, we can choose any number from 0 to 9, giving us 10 choices for each digit. So, the total number of seven-digit numbers where the leading digit is 2-9 is 8 * 10^6.
2. When the leading digit is 0 or 1:
If the leading digit is 0 or 1, there are no options for the remaining digits because we cannot repeat the leading digit. Therefore, the number of seven-digit numbers where the leading digit is 0 or 1 is 0.
To find the total number of seven-digit numbers, we sum up the two scenarios:
Total = 8 * 10^6 + 0 = 8 * 10^6.
Therefore, there are 8 million (8,000,000) seven-digit numbers where 0 and 1 cannot be the leading digit.