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Permutations, Combinations, Probability - Download Questions

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Re: P&C, Probability - Download [#permalink] New post 25 Oct 2009, 21:12
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eresh wrote:
I have a question regarding the #37 question and the answer given.

37. How many 5 digit numbers can be created if the following terms apply: the leftmost digit is even, the second is odd, the third is a non even prime and the fourth and fifth are two random digits not used before in the number?

a) 2520
b) 3150
c) 3360
d) 6000
e) 7500


37. The best answer is A.
The first digit has 4 options (2,4,6,8 and not 0), the second has 5 options (1,3,5,7,9) the third has 3 options (3,5,7 and not 2), the fourth has 7 options (10-3 used before) and the fifth has 6 options (10-4 used before). The total is 4*5*3*7*6=2520.


Now, it is not mentioned that a number cannot be repeated in for the 3rd digit. Say in the 2nd digit the number is 3 and so it is for the 3rd digit. The structure can be 233--, now for the 4th digit the option is 8 not 7.

Surely then the answer given is not right. But I don't know how to proceed further. Can someone please help? Or am I wrong about the porcess?


You are absolutely right. I'd say more there is no correct answer in choices. Surely the second and the third digits can be the same (in 3 cases out of 15) and in this case the number of possibilities for the 4th and 5th will be 8 and 7 and not 7 and 6.

So here is my solution:
1. second and third digits are the same:
4*3*1*8*7

2. second and third digits are not the same:
4*4*3*7*6

Total=4*3*1*8*7+4*4*3*7*6=2688

P.S. eresh, can you please post other questions (you consider as worth of discussion) in PS or DS forums, as not many check this tree for particular problems, but rather for the tips and tutorials. You may even duplicate this question as there could be other opinions about it. Thanks.
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Re: P&C, Probability - Download [#permalink] New post 25 Oct 2009, 21:46
Bunuel, I believe your solution is absolutely correct.

So here is my solution:
1. second and third digits are the same:
4*3*1*8*7

2. second and third digits are not the same:
4*4*3*7*6


Thinking of the approach, I understand that there are a total 15 combination of the 2nd and 3rd digit, of which in 3 combination the digits will be same. Therefore, there are 12 other possibilities where the digits are not same. The red part 4*3 also is equal to 12 but I could not figure out why it was 4*3 (My brains seems to stop working when I try to focus too much :D). Anyway, your answer seems correct and thank you for that.
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Re: P&C, Probability - Download [#permalink] New post 25 Oct 2009, 22:26
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Expert's post
eresh wrote:
Bunuel, I believe your solution is absolutely correct.

So here is my solution:
1. second and third digits are the same:
4*3*1*8*7

2. second and third digits are not the same:
4*4*3*7*6


Thinking of the approach, I understand that there are a total 15 combination of the 2nd and 3rd digit, of which in 3 combination the digits will be same. Therefore, there are 12 other possibilities where the digits are not same. The red part 4*3 also is equal to 12 but I could not figure out why it was 4*3 (My brains seems to stop working when I try to focus too much :D). Anyway, your answer seems correct and thank you for that.


Think about it this way: we don't want second and third digits to be the same, let's first choose the third digit(clearly it doesn't matter which one we choose first) how many possibilities are there? 3 (3 odd primes), than choose the second digit how many possibilities are there as one odd prime is already used? 5-1=4 --> 3*4=4*3.

Hope now it's clear.
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NEW TO MATH FORUM? PLEASE READ THIS: ALL YOU NEED FOR QUANT!!!

PLEASE READ AND FOLLOW: 11 Rules for Posting!!!

RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis NEW!!!; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) NEW!!!; 12. Tricky questions from previous years. NEW!!!;

COLLECTION OF QUESTIONS:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS ; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


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Re: P&C, Probability - Download [#permalink] New post 25 Oct 2009, 22:56
Bunuel wrote:

Think about it this way: we don't want second and third digits to be the same, let's first choose the third digit(clearly it doesn't matter which one we choose first) how many possibilities are there? 3 (3 odd primes), than choose the second digit how many possibilities are there as one odd prime is already used? 5-1=4 --> 3*4=4*3.

Hope now it's clear.


Ohh, Ok I got it now :lol:
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Re: P&C, Probability - Download [#permalink] New post 14 Nov 2009, 19:37
This looks great. Going to study hard on these. Thank you very much
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Re: P&C, Probability - Download [#permalink] New post 16 Nov 2009, 00:59
Kudos to Amardeep Sharma.
Look at the number of downloads, 1576 & 1185, and yet very few kudos.
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Re: P&C, Probability - Download [#permalink] New post 03 Dec 2009, 06:29
Kudos, i downloaded, and its great.

Also kudos to brunel, for coming up with that great explanation: brilliant. :)
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Re: P&C, Probability - Download [#permalink] New post 12 Mar 2010, 23:57
Thanks... Thats very useful
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Re: P&C, Probability - Download [#permalink] New post 16 Mar 2010, 08:29
Thank you!!! great resource
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Re: P&C, Probability - Download [#permalink] New post 24 Mar 2010, 19:10
whts the difference between the 2 files?
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Re: P&C, Probability - Download [#permalink] New post 02 Apr 2010, 07:28
Very useful- thanks for creating it!
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Re: P&C, Probability - Download [#permalink] New post 29 Apr 2010, 09:17
Great !!! This Is exactly what I needed.

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Re: P&C, Probability - Download [#permalink] New post 06 May 2010, 05:49
thanks for sharing, I will take a look at them
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Re: Permutations, Combinations, Probability - Download Questions [#permalink] New post 07 May 2010, 13:27
Thanks for the quiz.
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Re: Permutations, Combinations, Probability - Download Questions [#permalink] New post 08 May 2010, 13:09
thanks for the material !
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Re: Permutations, Combinations, Probability - Download Questions [#permalink] New post 09 May 2010, 14:19
thanks for the material
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Re: Permutations, Combinations, Probability - Download Questions [#permalink] New post 10 May 2010, 05:38
Thanks for the valuable post :)
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Re: Permutations, Combinations, Probability - Download Questions [#permalink] New post 13 May 2010, 01:43
Thanks a lot. Very much appreciated.

What is the difference between the two files except formatting?
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Re: Permutations, Combinations, Probability - Download Questions [#permalink] New post 13 May 2010, 08:38
Thanks I really need to work on probability this is of great help

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Re: Permutations, Combinations, Probability - Download Questions [#permalink] New post 15 May 2010, 21:33
thank you for sharing!!
Re: Permutations, Combinations, Probability - Download Questions   [#permalink] 15 May 2010, 21:33
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