How many integers greater than 1699 but not greater than 6000 can be formed using the digits 0, 1, 2, 3, 4, 5, 6 if repetitions are allowed? radio_button_unchecked 1715 radio_button_unchecked 1373 radio_button_unchecked 1716 radio_button_unchecked 2400
Question
How many integers greater than 1699 but not greater than 6000 can be formed using the digits 0, 1, 2, 3, 4, 5, 6 if repetitions are allowed?
radio_button_unchecked 1715
radio_button_unchecked 1373
radio_button_unchecked 1716
radio_button_unchecked 2400
Solution
To solve this problem, we need to consider the number of integers that can be formed with the given digits that are between 1700 and 6000.
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For the thousands place, we have 5 choices (1, 2, 3, 4, 5) because it cannot be 0 or 6 to stay within the range.
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For the hundreds place, we have 7 choices (0, 1, 2, 3, 4, 5, 6) because any of the given digits can be used.
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Similarly, for the tens and ones places, we also have 7 choices each.
So, the total number of integers that can be formed is 5 (for the thousands place) * 7 (for the hundreds place) * 7 (for the tens place) * 7 (for the ones place) = 1715.
So, the correct answer is 1715.
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