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Senior Manager
Joined: 25 Dec 2003
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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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CIO
Joined: 09 Mar 2003
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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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Manager
Joined: 16 May 2004
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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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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
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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.
P.S. If the question had read, what are the odd, then the answer would have been
4x4x4x4=256 right?
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Davefor MBA
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CIO
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almost. it would be 5x5x5x5, since the odds are 1,3,5,7,9 with no zero.
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Intern
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Great thanks. I miscounted earlier
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Davefor MBA
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close
