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Excluding numbers with leading 0s, there are 6804 such numbers.

Q: How many 5 digit numbers have exactly two sevens in them?

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Leaving out 077, since it is actually a two digit number, the answer is 35.

There are exactly 71 of them.

1

Exactly 2: 243 of them.

Exactly 3,628,800, or 10!.

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Leaving out 077, since it is actually a two digit number, the answer is 35.

27: 077,177,277,377,477,577,677,877,977,717,727,737,747,757,767,777,787,797

There are 6804 such numbers.

There are exactly 71 of them.

There aren't going to be any 7's in the hundreds digit, so first we look at how many there will be in the ones digit. Since there will be a 7 for every 10 numbers, and there are 501 numbers between 100 and 600 inclusive), we'll have floor(501 / 10) = 50 sevens in the ones digit. For the tens digit, we'll encounter 10 sevens for every 100, from 70 to 79, and so we have floor(501 / 100) = 5 times we'll have 70 - 79 so that's 5 * 10 = 50 sevens in the tens digit. However, we don't want to know how many sevens there are, we want to exclude overlaps. Thus we subtract every instance of 77 we see (overlap!), and we have floor(501 / 100) = 5 overlaps. 50 + 50 - 5 = 95, so a total of 95 numbers will have the digit 7 at least once.

the right answer is 10 cause there is o,1,2,3,4,5,6,7,8,9 so there 10 numbers in total which have 1 digit

If you include the number 3,000, there are exactly 2,001 4-digit numbers between 500 and 3000.

Exactly 2: 243 of them.

1

18

Exactly 3,628,800, or 10!.

There are 22680 numbers, excluding those with leading 0s.