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PERMUTATION PS 4 GMAT

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mand-y
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PERMUTATION PS 4 GMAT [#permalink] New post   11 Jan 2006, 06:25
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hello
PLZ explain your work

how many 5 DIGITS MUMBER EXIST IN WHICH AT LEAST ONE OF THE DIGIT REPEAT

thanksss



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Re: PERMUTATION PS 4 GMAT [#permalink] New post   11 Jan 2006, 06:38
The digits can be 0-9 -> 10 numbers

Case of repeat at least once:
Number of ways = 10P5/2! -> divide by 2! since 2 numbers will be repeaed

Case of repeat twice:
Number of ways = 10P5/3!

Case of repeat thrice:
Number of ways = 10P5/4!

Case of all same:
Number of ways = 1

Total number of ways = 10P5/2! + 10P5/3! + 10P5/4! + 1
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Re: PERMUTATION PS 4 GMAT [#permalink] New post   11 Jan 2006, 08:17
If I were to think of this in terms of

P(at least 1 repeat) = 1 - P(no repeats), how would I go about doing the calculation ?
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Re: PERMUTATION PS 4 GMAT [#permalink] New post   11 Jan 2006, 10:30
Can someone comment on my solution:

Number of ways to arrange five digits without worrying about repeatation is:
10*10*10*10*10.

Number of ways to arrange 5 digits without ANY repeats is 10*9*8*7*6.

Number of arrangements with at least ONE repeat is = 10^5 - (10*9*8*7*6).
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Re: PERMUTATION PS 4 GMAT [#permalink] New post   11 Jan 2006, 15:18
Number of ways to arrange five digits without worrying about repeatation is:
10*10*10*10*10.

shouldnt this be

9*10*10*10*10 coz the first digit can not be 0

???

Thanks
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Re: PERMUTATION PS 4 GMAT [#permalink] New post   Updated on: 11 Jan 2006, 16:52
Total 5 digit numbers = 10000 to 99999 inclusive i.e = 90000

For a number to be 5 digit, first digit can not be 0.

Now calculate that there are no repeats in a five digit number:
Number of ways first digit can be selected = 9
Number of ways second digit can be selected = 9
Number of ways third digit can be selected = 8
Number of ways fourth digit can be selected = 7
Number of ways fifth digit can be selected = 6

So numbers with no repeat = 9 * 9 * 8 * 7 * 6 = 27216

So numbers with atleast 1 digit repeated = 90000 - 27216 = 62784

Originally posted by ps_dahiya on 11 Jan 2006, 15:32.
Last edited by ps_dahiya on 11 Jan 2006, 16:52, edited 2 times in total.
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Re: PERMUTATION PS 4 GMAT [#permalink] New post   11 Jan 2006, 15:36
lhotseface wrote:
Can someone comment on my solution:

Number of ways to arrange five digits without worrying about repeatation is:
10*10*10*10*10.
Number of ways to arrange 5 digits without ANY repeats is 10*9*8*7*6.

Number of arrangements with at least ONE repeat is = 10^5 - (10*9*8*7*6).


In the first bold part you forgot that 00001 is not a 5 digit number. Five digits numbers are from 10000 to 99999 = 90000

In the second bold part you also forgot that first digit of a five digit number can not be zero so it should be 9*9*8*7*6
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Re: PERMUTATION PS 4 GMAT [#permalink] New post   11 Jan 2006, 17:32
:oops: Thanks !
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Re: PERMUTATION PS 4 GMAT [#permalink] New post   11 Jan 2006, 19:49
ps_dahiya wrote:
Total 5 digit numbers = 10000 to 99999 inclusive i.e = 90000

For a number to be 5 digit, first digit can not be 0.

Now calculate that there are no repeats in a five digit number:
Number of ways first digit can be selected = 9
Number of ways second digit can be selected = 9
Number of ways third digit can be selected = 8
Number of ways fourth digit can be selected = 7
Number of ways fifth digit can be selected = 6

So numbers with no repeat = 9 * 9 * 8 * 7 * 6 = 27216

So numbers with atleast 1 digit repeated = 90000 - 27216 = 62784


ps_dahiya, in your calculation for numbers with no repeat, should it not be 9x8x7x6x5 . You have 9x9, which indicates that there is a possibility that the first two numbers can be equal, right ?

Just checking .... i might be wrong
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Re: PERMUTATION PS 4 GMAT [#permalink] New post   11 Jan 2006, 22:25
pmenon wrote:
ps_dahiya wrote:
Total 5 digit numbers = 10000 to 99999 inclusive i.e = 90000

For a number to be 5 digit, first digit can not be 0.

Now calculate that there are no repeats in a five digit number:
Number of ways first digit can be selected = 9
Number of ways second digit can be selected = 9
Number of ways third digit can be selected = 8
Number of ways fourth digit can be selected = 7
Number of ways fifth digit can be selected = 6

So numbers with no repeat = 9 * 9 * 8 * 7 * 6 = 27216

So numbers with atleast 1 digit repeated = 90000 - 27216 = 62784


ps_dahiya, in your calculation for numbers with no repeat, should it not be 9x8x7x6x5 . You have 9x9, which indicates that there is a possibility that the first two numbers can be equal, right ?

Just checking .... i might be wrong


I don't think so.

First digit can be 1 to 9 = 9
Second digit can be 0-9 = 10 but can not be one that has been selected as first digit. So = 9
Third digit can be 0-9 = 10 but can not be ones those have been selected as first and second digit. So = 8 and so on.

Am I right guys?
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Re: PERMUTATION PS 4 GMAT [#permalink] New post   11 Jan 2006, 23:28
yups i too got 62784...going by ps logic...



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Re: PERMUTATION PS 4 GMAT [#permalink]
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