Consider the three-digit numerals: 100 to 999.

a) How many have at least one 8?

b) How many have at least one 0 or at least one 8?

c) How many have at least one 0 and at least one 8?

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- Jul 27th 2009, 05:16 PMkimberlyd1020Inclusion-exclusion
Consider the three-digit numerals: 100 to 999.

a) How many have at least one 8?

b) How many have at least one 0 or at least one 8?

c) How many have at least one 0 and at least one 8? - Jul 28th 2009, 02:45 AMPlato
Part a) Let’s find the number which contains no digit 8. The first digit can be anyone of 1,2,3,4,5,6,7, or 9. Then the other two digits can be anyone of 0,1,2,3,4,5,6,7, or 9.

So there are $\displaystyle (8\cdot 9\cdot 9)=648$ that do not have a digit 8.

So how many do contain at least one eight?

Now you try the others.