Math CentralQuandaries & Queries


Question from Lacy:

Using the digits zero through nine, how many two-digit numbers can be formed,which do not have a four or five?

Hi Lacy,

If 4 and 5 are not allowed then you have 8 digits to work with. The digit 0 is special so I'm going to deal with it later. With these restrictions you want to create two digit numbers using 1, 2, 3, 6, 7, 8 and 9, that's seven digits.

With these restrictions you have seven digits to choose from for the tens digit and seven digits to choose from for the units digit. Hence you can create $7 \times 7$ two digit numbers using the digits 1, 2, 3, 6, 7, 8 and 9.

Now consider the situation where at least one of the digits can be 0. The tens digit can't be 0 or you only have a one digit number so the only two digit numbers you can create from 0, 1, 2, 3, 6, 7, 8 and 9 are 10, 20, 30, 60, 70, 80, and 90.


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