# How many integers from 100 through 999, inclusive,do not contain any of the digits 2,3,4 or 5?

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- polluxLv 41 decade agoFavorite Answer
The number of such numbers is 180. Here's one way to see it.

The numbers 100 to 999 are all three-digit numbers and without any restrictions, there are 10 values that each digit can take 0 thru 9. The number of numbers 0 thru 999 is obviously 10 x 10 x 10 = 1000. If we restrict the digits to 0,1,6,7,8,9 as this problem does, however, that's six possible digits, so the number of possible numbers 0 to 999 is 6 x 6 x 6 = 216, but 6 x 6 = 36 of those are between 0 and 99. Since we start with 100, we must subtract that number 36 from 216, which gives 180.

There must be an easier way to explain this. ;-)

Source(s): My brain. ;-) - Anonymous1 decade ago
180

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