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How many numbers of 7 digits can be formed from the digits

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Manager
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How many numbers of 7 digits can be formed from the digits [#permalink] New post 10 Aug 2007, 03:23
How many numbers of 7 digits can be formed from the digits 1,2,3,4,5,6,7 if there are not more than 2 digits between 1 and 2 ?

Please provide an explanation along with the solution. :-D
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Re: Nice P&C Question [#permalink] New post 10 Aug 2007, 06:45
ajay_gmat wrote:
How many numbers of 7 digits can be formed from the digits 1,2,3,4,5,6,7 if there are not more than 2 digits between 1 and 2 ?

Please provide an explanation along with the solution. :-D


Two digits between 1 and 2
1XX2XXX = 2*5!
X1XX2XX = 2*5!
XX1XX2X = 2*5!
XXX1XX2 = 2*5!

One digit between 1 and 2
1X2XXXX = 2*5!
X1X2XXX = 2*5!
XX1X2XX = 2*5!
XXX1X2X = 2*5!
XXXX1X2 = 2*5!

Total = 9*2*5! = 2160
Manager
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Re: Nice P&C Question [#permalink] New post 10 Aug 2007, 07:46
bkk145 wrote:
ajay_gmat wrote:
How many numbers of 7 digits can be formed from the digits 1,2,3,4,5,6,7 if there are not more than 2 digits between 1 and 2 ?

Please provide an explanation along with the solution. :-D


Two digits between 1 and 2
1XX2XXX = 2*5!
X1XX2XX = 2*5!
XX1XX2X = 2*5!
XXX1XX2 = 2*5!

One digit between 1 and 2
1X2XXXX = 2*5!
X1X2XXX = 2*5!
XX1X2XX = 2*5!
XXX1X2X = 2*5!
XXXX1X2 = 2*5!

Total = 9*2*5! = 2160


Thanks bkk145 for your reply. Could you explain why you are multiplying by 2 each time ? The Question says between 1 and 2 and i hence think that 1 and 2 are not interchangeable .. Any thoughts, am not sure myself ?
VP
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Re: Nice P&C Question [#permalink] New post 10 Aug 2007, 08:01
ajay_gmat wrote:
bkk145 wrote:
ajay_gmat wrote:
How many numbers of 7 digits can be formed from the digits 1,2,3,4,5,6,7 if there are not more than 2 digits between 1 and 2 ?

Please provide an explanation along with the solution. :-D


Two digits between 1 and 2
1XX2XXX = 2*5!
X1XX2XX = 2*5!
XX1XX2X = 2*5!
XXX1XX2 = 2*5!

One digit between 1 and 2
1X2XXXX = 2*5!
X1X2XXX = 2*5!
XX1X2XX = 2*5!
XXX1X2X = 2*5!
XXXX1X2 = 2*5!

Total = 9*2*5! = 2160


Thanks bkk145 for your reply. Could you explain why you are multiplying by 2 each time ? The Question says between 1 and 2 and i hence think that 1 and 2 are not interchangeable .. Any thoughts, am not sure myself ?


Actually they are interchangeable. Digits between 1 and 2 means any number between those two, but it does not restrict that 1 and 2 cannot be interchangeable. You can have 1342 or 2341; hence you must multiple by 2 each time.
I hope the number I got was the right answer.
Re: Nice P&C Question   [#permalink] 10 Aug 2007, 08:01
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How many numbers of 7 digits can be formed from the digits

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