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How many odd three-digit integers greater than 800 are there

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How many odd three-digit integers greater than 800 are there [#permalink] New post 11 Nov 2008, 02:40
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How many odd three-digit integers greater than 800 are there such that all their digits are different?

a) 40
b) 56
c) 72
d) 81
e) 104




Please explain your answer.
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Re: PS: How many odd three-digit integers [#permalink] New post 11 Nov 2008, 02:59
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C

1. Let's consider 8xy set
2. y e [1,3,5,7,9] (5 possibilities), x has 10 possibilities - 2 possibilities (8 and y). The total number is 5*8=40
3. Let's consider 9xy set
4. y e [1,3,5,7] (4 possibilities), x has 10 possibilities - 2 possibilities (9 and y). The total number is 4*8=32
5 40+32=72
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Re: PS: How many odd three-digit integers [#permalink] New post 11 Nov 2008, 08:48
Walker,
great explanation. Thanks.
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Re: PS: How many odd three-digit integers [#permalink] New post 12 Nov 2008, 03:56
walker wrote:
C

1. Let's consider 8xy set
2. y e [1,3,5,7,9] (5 possibilities), x has 10 possibilities - 2 possibilities (8 and y). The total number is 5*8=40
3. Let's consider 9xy set
4. y e [1,3,5,7] (4 possibilities), x has 10 possibilities - 2 possibilities (9 and y). The total number is 4*8=32
5 40+32=72



Great explanation walker! Thanks. The OA is C. I just have 1 question. Why did you have to start first from the left digit, then skipped the middle digit to go to the right digit, then back to the middle digit? Why couldn't you just go from left to middle, then from middle to right?

thanks
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Re: PS: How many odd three-digit integers [#permalink] New post 12 Nov 2008, 04:13
I saw that we have two different cases here: 8 and 9. 9 is odd and we cannot choose 9 as a unit digit. 8 is even and don't add a restriction to a unit digit. That is why I started with division of the problem by two cases: 8xy and 9xy
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Re: PS: How many odd three-digit integers [#permalink] New post 12 Nov 2008, 04:18
walker wrote:
I saw that we have two different cases here: 8 and 9. 9 is odd and we cannot choose 9 as a unit digit. 8 is even and don't add a restriction to a unit digit. That is why I started with division of the problem by two cases: 8xy and 9xy


as always, you never failed to answer my questions. you're a legend ;)
thanks!
Re: PS: How many odd three-digit integers   [#permalink] 12 Nov 2008, 04:18
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