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baily106
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Integers & Digits

by baily106 Sat Jul 26, 2014 11:59 am

Hello,

I am referring to question #8 on page 297 of The Official Guide. The question reads "how many 3-digit positive integers are odd and do not contain the digit 5?" There is no explanation provided for the answer.

Thanks.
tommywallach
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Re: Integers & Digits

by tommywallach Fri Aug 01, 2014 10:32 pm

Hey Baily,

This is a combinatorics question, so we would use the slots method:

_ _ _

Three slots for the three digits.

8 _ _

Eight choices for the first slot (because it can't be 5, and it can't be 0, because a three-digit number can't start with a 0).

8 9 _

Nine choices for the second slot, because we can choose any number except 5.

8 9 4

Only four choices for the third slot, because it can't end in 5, but it must be odd, meaning it must end in 1, 3, 7, or 9.

8 * 9 * 4 = 288

-t
baily106
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Re: Integers & Digits

by baily106 Sun Aug 03, 2014 10:53 am

That's pretty simple; thank you.
tommywallach
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Posts: 1917
Joined: Thu Mar 31, 2011 11:18 am
 

Re: Integers & Digits

by tommywallach Wed Aug 06, 2014 9:18 pm

Glad to help!