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How many 5 digit ( digit = 0 - 9 ) zip codes can exist in wh

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How many 5 digit ( digit = 0 - 9 ) zip codes can exist in wh [#permalink] New post 10 Nov 2009, 09:47
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How many 5 digit ( digit = 0 - 9 ) zip codes can exist in which atleast one digit is repeated ?
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Re: Zip Code question [#permalink] New post 10 Nov 2009, 10:03
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HopefulOldie wrote:
How many 5 digit ( digit = 0 - 9 ) zip codes can exist in which atleast one digit is repeated ?


Zip codes with 5 digits (all five digits can be repeated): 10^5=100,000

Zip codes with no digit being repeated: 10*9*8*7*6=30,240

Zip codes with at least one digit being repeated: 100,000-30,240=69,760
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Re: Zip Code question [#permalink] New post 10 Nov 2009, 10:37
Bunuel wrote:
HopefulOldie wrote:
How many 5 digit ( digit = 0 - 9 ) zip codes can exist in which atleast one digit is repeated ?


Zip codes with 5 digits (all five digits can be repeated): 10^5=100,000 if first digit is 0, its no longer 5-digit right?

Zip codes with no digit being repeated: 10*9*8*7*6=30,240 if first digit is 0, its no longer 5-digit right?

Zip codes with at least one digit being repeated: 100,000-30,240=69,760


so isn't the answer

Zip codes with 5 digits (all five digits can be repeated): 9 * 10 ^4 = 90000
Zip codes with no digit being repeated: 9*9*8*7*6 = 27216

Zip codes with at least one digit being repeated: 90000-27216 = 62784 ?
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Last edited by srini123 on 10 Nov 2009, 11:15, edited 1 time in total.
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Re: Zip Code question [#permalink] New post 10 Nov 2009, 10:39
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You got it ... BINGO !!!

Manager,

You are pretty close but the zip codes can start with 0.


Total combination for zip code = 10 * 10 * 10 * 10 * 10 ( A )

Total combinations without single digit repeated = 10 * 9 * 8 * 7 * 6 ( B )

Answer : A - B

For those who have taken GMAT do you think this is a 600 or a 700 level question.

Last edited by HopefulOldie on 10 Nov 2009, 11:00, edited 2 times in total.
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Re: Zip Code question [#permalink] New post 10 Nov 2009, 10:47
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srini123 wrote:
so isn't the answer

Zip codes with 5 digits (all five digits can be repeated): 9 * 10 ^4 = 90000
Zip codes with no digit being repeated: 9*9*8*7*6 = 27216

Zip codes with at least one digit being repeated: 90000-272162784 ?


I don't think this should be the case:

5 digit ZIP code is different from 5 digit number, I suppose. 5 digit number can not start with 0, as it becomes 4 digit in this case but 5 digit ZIP code can be 01234. Meaning that if we take zip code of a credit card, it can start with 0 eg 01234 and still be 5 digit.

What's OA for this question?
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Re: Zip Code question [#permalink] New post 10 Nov 2009, 11:16
Cool, now I see, zip code is a code and not a number - OMG how many things we need to keep track of ... its real scary out there :)

Thanks Bunuel
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Re: Zip Code question [#permalink] New post 13 May 2011, 01:13
All possibilities - No digit is repeated

= (10 * 10 * 10 * 10 * 10) - (6 *7 * 8 * 9 * 10)

= 100000 - 42 * 720

= 100000 - 30240

= 69760
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Re: Zip Code question [#permalink] New post 13 May 2011, 12:30
I think it should be mentioned that Zip Code can start with 0.
Which is the case I have never seen in India.

How was we suppose to know this Universal Rule?
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Re: How many 5 digit ( digit = 0 - 9 ) zip codes can exist in wh [#permalink] New post 20 Jul 2014, 00:42
Bunuel wrote:
HopefulOldie wrote:
How many 5 digit ( digit = 0 - 9 ) zip codes can exist in which atleast one digit is repeated ?


Zip codes with 5 digits (all five digits can be repeated): 10^5=100,000

Zip codes with no digit being repeated: 10*9*8*7*6=30,240

Zip codes with at least one digit being repeated: 100,000-30,240=69,760



Ways to arrange 5 digits = 10^5

Ways to arrange (no repetitions) = 10*9*8*7*6 = 30240

At-least one repetition: (10^5) - 30240 = 69760

Is this also right?
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Re: How many 5 digit ( digit = 0 - 9 ) zip codes can exist in wh [#permalink] New post 20 Jul 2014, 03:20
Expert's post
hamzakb wrote:
Bunuel wrote:
HopefulOldie wrote:
How many 5 digit ( digit = 0 - 9 ) zip codes can exist in which atleast one digit is repeated ?


Zip codes with 5 digits (all five digits can be repeated): 10^5=100,000

Zip codes with no digit being repeated: 10*9*8*7*6=30,240

Zip codes with at least one digit being repeated: 100,000-30,240=69,760



Ways to arrange 5 digits = 10^5

Ways to arrange (no repetitions) = 10*9*8*7*6 = 30240

At-least one repetition: (10^5) - 30240 = 69760

Is this also right?


Isn't this exact same approach as mine?
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PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS ; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


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Re: How many 5 digit ( digit = 0 - 9 ) zip codes can exist in wh   [#permalink] 20 Jul 2014, 03:20
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