HOW MANY SEVEN-DIGIT NUMBERS LESS THAN 1,048,000 CAN BE MADE USING THE DIGITS 0,1,4,6,7,8,AND 9? THINK: MAKE A LIST OF POSSIBLE WAYS TO REPRESENT YOUR SEVEN-DIGIT NUMBERS
since the number must be < 1 048 000
the number must be like
104ABCD where A can only be 6 or 7
so the ABCD part can be filled in
2x3x2x1 or 12 ways
I will leave it up to you to list those 12 numbers.
Go about it systematically
e.g.
1046789
1046798
1046879
1046897 etc
To determine the number of seven-digit numbers that can be made using the given digits (0, 1, 4, 6, 7, 8, and 9) and are less than 1,048,000, we can follow these steps:
1. Identify the constraints for each digit's position:
- The first digit cannot be zero since it would result in a number with fewer than seven digits.
- The second digit does not have any specific constraints.
- The remaining five digits can be any of the given digits (0, 1, 4, 6, 7, 8, 9).
2. Create a list of possible combinations for each position:
- For the first digit, we have six options (1, 4, 6, 7, 8, 9).
- For the second digit, we have seven options available since zero is now included.
3. Calculate the number of possible combinations:
- Multiply the number of possibilities for each digit's position together to get the total count.
Let's go through the steps and calculate the number of seven-digit numbers less than 1,048,000.
Step 1: Constraints
- The first digit: 6 options (1, 4, 6, 7, 8, 9)
- The second digit: 7 options (0, 1, 4, 6, 7, 8, 9)
- The remaining five digits: 7 options each
Step 2: Create combinations
- For the first digit, we have six choices: {1, 4, 6, 7, 8, 9}.
- For the second digit, we have seven choices: {0, 1, 4, 6, 7, 8, 9}.
- For the remaining five digits, we have seven choices each: {0, 1, 4, 6, 7, 8, 9}.
Step 3: Calculate the number of combinations
- Multiply the number of choices for each digit's position together:
6 choices for the first digit * 7 choices for the second digit * 7 choices for the third digit * 7 choices for the fourth digit * 7 choices for the fifth digit * 7 choices for the sixth digit * 7 choices for the seventh digit
The total count can be calculated as:
6 * 7 * 7 * 7 * 7 * 7 * 7 = 205,752
Therefore, there are 205,752 seven-digit numbers that can be made using the given digits and are less than 1,048,000.