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Answer :
There are 0 numbers between 7000 and 8000 that contain at least one 9.
To find the count of numbers between 7000 and 8000 containing at least one 9, we can subtract the count of numbers that do not contain any 9 from the total count of numbers between 7000 and 8000.
The total count of numbers between 7000 and 8000 is 1000 (8000 - 7000 = 1000).
The count of numbers that do not contain any 9 is also 1000. This is because we have 9 choices (0-8) for each digit in the thousands, hundreds, tens, and units place, giving us a total of 9 * 9 * 9 * 9 = 6561 numbers. However, we need to exclude the numbers that are less than 7000, so we subtract 561 from 6561, resulting in 6000 numbers.
Therefore, the count of numbers between 7000 and 8000 containing at least one 9 is 1000 - 1000 = 0.
Learn more about counting numbers with a specific digit here:
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Final answer:
There are 271 numbers between 7000 and 8000 that contain at least one '9'. This is found by subtracting the count of numbers without a '9' (729) from the total numbers in the range (1000).
Explanation:
To calculate the number of numbers between 7000 and 8000 that contain at least one '9', we can first determine the total number of numbers in this range and then subtract the numbers that do not contain a '9'. The total numbers in this range are 1000 (from 7001 up to and including 7999). To find the numbers without a '9', consider that each digit (the thousands, hundreds, tens, and units place) can be 0-9, excluding 9 which gives us 9 choices per digit. Since the first digit is fixed at '7', we only have three more digits to consider, which gives us 9*9*9 = 729 combinations without a '9'. Therefore, the count of numbers with at least one '9' would be 1000 - 729 = 271.
