How many 5 digit (digit = 0 - 9) zip codes can exist in which at least

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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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 ?

Major Shareholder

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.

I don't think this should be the case:

5 digit ZIP code is different from 5 digit number, I suppose. 5 digit number cannot 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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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

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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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?

Can we have 0 in in the first place of a zipcode?

We are not told 5-digit number, so yes.
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Ahhh, the term "number"... Thanks.. I'll keep that in mind.

Asked: How many 5 digit ( digit = 0 - 9 ) zip codes can exist in which atleast one digit is repeated ?[/quote]

Total 5 digits codes = 10^5 = 100000

5 digit cods where no digit is repeated = 10*9*8*7*6 = 30240

The number of 5 digit ( digit = 0 - 9 ) zip codes can exist in which atleast one digit is repeated = 100000 - 30240 = 69760

Why is this logic is incorrect for this question? Can you help me?
10*9*8*7*1 = 5040
Since we have 10 digits for first one, 9 for second and so on and the fifth should be the one, since is should repat other.

The key to solving the equation is thinking other way around and getting the answer by the following methid
The total no of combination of both repeated and non repeated terms = (10)^5 = 100000
The total no of combination of non repeated terms= 10*9*8*7*6=30240
The total no of combination of repeated terms with at least one digit = 100000-30240=69760
Hence IMO C

Hi Bunuel,
Can you help me understand the gap in my thinking?

I did 10*10*10*10*9
I thought the first 4 digits can be any one of the 10 digits and the last digit has to repeat any of those so I thought it could be 9.

But now I understand if say the first few numbers are 0123 the 5th number has to be one of these 4 numbers for at least one to repeat.
I forget to take the total possibilities - possbilities not required in these sort of questions.

Aishyk97

A simple trick to answer combination/probability questions such as the above would be to take note of the word "at least"

Typically, for such questions, it is always easier arrive at the answer by taking total number of possibilities and subtracting from it the complement of what we are asked.

In the above question, we are asked to find zip codes where at least one digit is repeated. Therefore, from the total number of possible zip codes, we need to subtract number of zip codes where NONE of the digits are repeated.

Here is how your login in taking 10*10*10*10*9 is wrong:

1st digit: 10 options - Say we choose 1
2nd digit: 10 options - Say we choose 2
3rd digit: 10 options - Say we choose 3
4th digit: 10 options - Say we choose 4
5th digit: 9 options. I can choose the number 5 and the resulting number i.e. 12345 has 5 different digits. While I could've chosen the number 3 in which case the one of the digits would've been repeated, I can still choose other digits wherein all digits of the zip code will not have any repeated numbers.

Hope you've understood. All the best, Cheers