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kevincan
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Larry tried to type his new 7-digit phone number on a form, 18 Apr 2007, 08:50
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Larry tried to type his new 7-digit phone number on a form, but what appeared on the form was 39269, since the '4' key on his computer no longer works. His secretary has decided to make a list of all of the numbers that could be Larry's new number. How many numbers will there be on the list?

(A) 21 (B) 24 (C) 25 (D) 30 (E) 36



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KillerSquirrel
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Larry tried to type his new 7-digit phone number on a form, Updated on: 19 Apr 2007, 02:34
Originally posted by KillerSquirrel on 18 Apr 2007, 10:27.
Last edited by KillerSquirrel on 19 Apr 2007, 02:34, edited 2 times in total.
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Since there are 5 fixed numbers - 39269 we need to plug in 4,4

if we had to plug only one 4 - we had six ways:

439269

349269

and so on ...

since we need to plug in 4,4 - we can use one 4 as fixed hence:

4439269

4349269

snd so on ...

(*)

see followup post - my reasoning here is wrong - its a combination problem ! hence - 21
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Larry tried to type his new 7-digit phone number on a form, 18 Apr 2007, 10:53
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the length of the list cannot be determined without knowledge of larry's secretary skills.... will the secretary find all 36 posible numbers? will he, mistakenly, write on the list the same number more than once?

just kidding....
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KillerSquirrel
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Larry tried to type his new 7-digit phone number on a form, 18 Apr 2007, 11:08
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hobbit
the length of the list cannot be determined without knowledge of larry's secretary skills.... will the secretary find all 36 posible numbers? will he, mistakenly, write on the list the same number more than once?

just kidding....
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I think it's not PC to say secretary , you should say "personal assistant" or "administrative assistant" :-D
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Larry tried to type his new 7-digit phone number on a form, 18 Apr 2007, 15:29
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Can someone explain this in another way pls? I am a bit confused? How do you know if it combination or permutation? Help!!! :cry: :(
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Larry tried to type his new 7-digit phone number on a form, 18 Apr 2007, 21:18
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kevincan
Larry tried to type his new 7-digit phone number on a form, but what appeared on the form was 39269, since the '4' key on his computer no longer works. His secretary has decided to make a list of all of the numbers that could be Larry's new number. How many numbers will there be on the list?

(A) 21 (B) 24 (C) 25 (D) 30 (E) 36
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There are 2 missing 4s. It is a 7 digit number. Total number of spots that you can chose for 4s in these 7 digits is 7C2 = 21 (we are using combinations as there is no difference between two 4s) Once we have chosen where we want to put 4s, all remaining digits will occupy the remaining slots.

Answer A
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Larry tried to type his new 7-digit phone number on a form, 19 Apr 2007, 01:19
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4 in the first place = 6 ways
4439269, 4349269, 4394269...etc.

4 in the second place = 5 ways
3449269, 3494269..etc.

4 in the third place = 4 ways

and so on.

6+5+4+3+2+1=21

A.
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Larry tried to type his new 7-digit phone number on a form, 19 Apr 2007, 02:31
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techjanson
kevincan
Larry tried to type his new 7-digit phone number on a form, but what appeared on the form was 39269, since the '4' key on his computer no longer works. His secretary has decided to make a list of all of the numbers that could be Larry's new number. How many numbers will there be on the list?

(A) 21 (B) 24 (C) 25 (D) 30 (E) 36

There are 2 missing 4s. It is a 7 digit number. Total number of spots that you can chose for 4s in these 7 digits is 7C2 = 21 (we are using combinations as there is no difference between two 4s) Once we have chosen where we want to put 4s, all remaining digits will occupy the remaining slots.

Answer A
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I stand corrected :oops: the answer is indeed - 21
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Larry tried to type his new 7-digit phone number on a form, 19 Apr 2007, 09:35
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Hi
I think that the ans is 36
We can put the 4 in 6 places. Since we need 2 4's then this can be done in 36 ways
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Larry tried to type his new 7-digit phone number on a form, 19 Apr 2007, 13:02
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techjanson
kevincan
Larry tried to type his new 7-digit phone number on a form, but what appeared on the form was 39269, since the '4' key on his computer no longer works. His secretary has decided to make a list of all of the numbers that could be Larry's new number. How many numbers will there be on the list?

(A) 21 (B) 24 (C) 25 (D) 30 (E) 36

There are 2 missing 4s. It is a 7 digit number. Total number of spots that you can chose for 4s in these 7 digits is 7C2 = 21 (we are using combinations as there is no difference between two 4s) Once we have chosen where we want to put 4s, all remaining digits will occupy the remaining slots.

Answer A
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Agree it is a comibination problem.

Nos of phone num = 7 *6/2 =21
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kumarajeet06
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Larry tried to type his new 7-digit phone number on a form, 19 Apr 2007, 14:12
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there are 7 possible space where 4 can be placed and it is clear from the method that there are two 4's in number so number of ways is 7C2 =21
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ywilfred
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Larry tried to type his new 7-digit phone number on a form, 19 Apr 2007, 18:45
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All we need to know is 'how to arrange two 4 in 7 spaces'. This is a combination question. So 7C2 will solve the problem.
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ninomoi
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Larry tried to type his new 7-digit phone number on a form, 19 Apr 2007, 20:14
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Thanks guys. NOw I get it :-D



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