How many seven - digit numbers less than 1,048,000 can be made using the digits 0,1,4,6,7,8 and 9
To find the number of seven-digit numbers less than 1,048,000 that can be made using the digits 0, 1, 4, 6, 7, 8, and 9, we need to consider the restrictions and constraints.
Step 1: Count the number of choices for each digit in the seven-digit number.
- The first digit cannot be zero (0), so we have 6 choices (1, 4, 6, 7, 8, 9).
- For the remaining digits (2nd to 7th), we have 7 choices (0, 1, 4, 6, 7, 8, 9) as the restriction doesn't apply to them.
Step 2: Multiply the number of choices for each digit together.
- There are 6 choices for the first digit, and 7 choices for each of the remaining six digits.
- Thus, the total number of seven-digit numbers that can be made is 6 * 7 * 7 * 7 * 7 * 7 * 7.
Step 3: Calculate the result.
- Evaluate the expression: 6 * 7 * 7 * 7 * 7 * 7 * 7.
- The result is 6 * 7^6, which equals 6 * 7^6 = 6 * 117,649 = 705,894.
Therefore, there are 705,894 seven-digit numbers less than 1,048,000 that can be made using the digits 0, 1, 4, 6, 7, 8, and 9.