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Senior Manager
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Numbers [#permalink] New post 15 Jul 2004, 05:30
Can anyone explain, how to solve such problems.

How many 4-digit positive integers are there in which all 4 digits are even?

A. 700
B. 500
C. 400
D. 300
E. 200


Please explain. Thanks
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 [#permalink] New post 15 Jul 2004, 05:43
Hi Carson,

The answer's B, 500.

A four digit number will have four places, and there are 5 even digits to distribute. Only 2,4,6,8 can go in the first place, but after that, all five, including zero, can be placed.

So the answer is 4x5x5x5, or 500.
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ans b [#permalink] New post 15 Jul 2004, 05:46
I'm thinking B.

so in a 4 digit number for all digits to be even

for the units place we have 5 options 0,2,4,6,8
similarly for 10s and 100s place to we have 5 options
for the thosands place we have 4 options 2,4,6,8
so the total number is 4 * 5 * 5 * 5 = 500
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 [#permalink] New post 15 Jul 2004, 05:56
Cool

Thats the answer 500. Man, sometimes it just needs few seconds of patient thinking. I was looking at probablity stuff and getting deep in to it.

Thanks for enlighting me.
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 [#permalink] New post 15 Jul 2004, 11:40
Wonderful!

I was looking for a shorcut for this for quite a while and your explanation was the best I've ever seen.

P.S. If the question had read, what are the odd, then the answer would have been

4x4x4x4=256 right?
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 [#permalink] New post 15 Jul 2004, 11:47
almost. it would be 5x5x5x5, since the odds are 1,3,5,7,9 with no zero.
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 [#permalink] New post 15 Jul 2004, 11:54
Great thanks. I miscounted earlier
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  [#permalink] 15 Jul 2004, 11:54
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