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# Numbers

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Senior Manager
Joined: 25 Dec 2003
Posts: 360
Location: India
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Numbers [#permalink]  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

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CIO
Joined: 09 Mar 2003
Posts: 463
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Hi Carson,

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.
Manager
Joined: 16 May 2004
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Location: columbus
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ans b [#permalink]  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
Senior Manager
Joined: 25 Dec 2003
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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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Intern
Joined: 07 Jun 2004
Posts: 29
Location: Sunnyvale
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Wonderful!

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

4x4x4x4=256 right?
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Davefor MBA

CIO
Joined: 09 Mar 2003
Posts: 463
Followers: 2

Kudos [?]: 35 [0], given: 0

almost. it would be 5x5x5x5, since the odds are 1,3,5,7,9 with no zero.
Intern
Joined: 07 Jun 2004
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Location: Sunnyvale
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Great thanks. I miscounted earlier
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Davefor MBA

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