Re: How many 3-digit positive integrs are odd and do not contain the digit "5"?
- From: "The Qurqirish Dragon" <qurqirishd@xxxxxxx>
- Date: 26 Dec 2005 06:50:38 -0800
me wrote:
> Thanks.
>
> I was thinking to get all the possible numbers and then subtract the
> ones with 5. Pbviously, that kind of approcah would not be the way to
> go about probability. I need to change my thinking pattern.
That would also work, but it would have entailed more work:
there are 900 3-digit integers.
a) 100 of them have a 5 in the hundreds' place
b) 90 of them have a 5 in the tens' place
c) 540 have a 5 or an even digit in the ones place
10 fall into categories a & b
60 fall into categories a & c
54 fall into categories b & c
6 fall into all three categories.
by inclusion-exclusion, the total number that have a 5 or are odd is:
100 + 90 + 540 -10 -60 -54 +6= 612
So the number that don't is 900 - 612 = 288 (which is the same answer
as above)
As I said, this is much longer, but still works.
.
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