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Desperate to know....

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by lechefrene » Mon Sep 01, 2008 8:07 am
...how many 5 digit numbers can be formed from a set of seven digits, without repeating digits, and not transposing numbers? For example, if I have the digits 1234567, how many five digit numbers can be formed? 12345, 23456, 34567, etc. are good numbers, but 54321 would not be valid as it is the same as 12345...also, 11234 is invalid as it repeats the digit 1. Please answer ASAP, and thanks so much in advance! ~lechefrene~
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Re: Desperate to know....

by parallel_chase » Mon Sep 01, 2008 8:21 am
lechefrene wrote:...how many 5 digit numbers can be formed from a set of seven digits, without repeating digits, and not transposing numbers? For example, if I have the digits 1234567, how many five digit numbers can be formed? 12345, 23456, 34567, etc. are good numbers, but 54321 would not be valid as it is the same as 12345...also, 11234 is invalid as it repeats the digit 1. Please answer ASAP, and thanks so much in advance! ~lechefrene~
1,2,3,4,5,6,7

7*6*5*4*3 = 2520 digits can be formed

Alternatively

you can use the permutation formula

7P5 = 7!/2! = 2520


Let me know if you have any doubts.
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Re: Desperate to know....

by 4meonly » Mon Sep 01, 2008 9:22 am
lechefrene wrote: but 54321 would not be valid as it is the same as 12345...also,
u mean order is not important?
i'll have 21 combinations

It seems to me that order is important! You'll have 2520 variants
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by lechefrene » Mon Sep 01, 2008 9:54 am
I don't think 2520 would be the right answer, but thanks so much for replying so quickly!

Also, I'm thinking 21 would be closer to the number I'm looking for. I came up with 19. Can you please post the numbers you came up with? Thanks a bunch!

~lechefrene~
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Re: Desperate to know....

by Ian Stewart » Mon Sep 01, 2008 9:56 am
lechefrene wrote:...how many 5 digit numbers can be formed from a set of seven digits, without repeating digits, and not transposing numbers? For example, if I have the digits 1234567, how many five digit numbers can be formed? 12345, 23456, 34567, etc. are good numbers, but 54321 would not be valid as it is the same as 12345...also, 11234 is invalid as it repeats the digit 1. Please answer ASAP, and thanks so much in advance! ~lechefrene~
I'll explain in three different ways:

The digits in the number must be in ascending order- that is, they must be in one particular order. If we could put the five digits we select in any order, the answer would be 7*6*5*4*3. However, for any set of five digits we choose, only one of the 5! orders we can put five digits in is acceptable. So we need to divide this by 5!, which gives 21.

Equivalently- once you choose a set of five digits, you must put them in ascending order to make an acceptable number, so the answer will be 7C5 = 7*6/2 = 21.

Or, you can just think of how many ways you could remove two digits from 1234567. For any pair you remove, you will get a different 5-digit number with digits in ascending order, and we can choose a pair of digits in 7C2 ways, or 21 ways.
For online GMAT math tutoring, or to buy my higher-level Quant books and problem sets, contact me at ianstewartgmat at gmail.com

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