Author 
Message 
TAGS:

Hide Tags

Intern
Joined: 10 Oct 2010
Posts: 6

If the letters a, A, b, B, c, and C are arranged at random in a row
[#permalink]
Show Tags
14 Oct 2010, 08:14
Question Stats:
0% (00:00) correct 100% (03:05) wrong based on 4 sessions
HideShow timer Statistics
If the letters a, A, b, B, c, and C are arranged at random in a row, what is the probability that the lower case letter appear in increasing alphabetical order?



Math Expert
Joined: 02 Sep 2009
Posts: 47200

Re: If the letters a, A, b, B, c, and C are arranged at random in a row
[#permalink]
Show Tags
14 Oct 2010, 08:20
abeer16 wrote: If the letters a, A, b, B, c, and C are arranged at random in a row, what is the probability that the lower case letter appear in increasing alphabetical order? Three letters a, b, and c can be arranged in 3!=6 different ways and only one of them will be in increasing alphabetical order, namely: abc, so P=1/6.
_________________
New to the Math Forum? Please read this: Ultimate GMAT Quantitative Megathread  All You Need for Quant  PLEASE READ AND FOLLOW: 12 Rules for Posting!!! Resources: GMAT Math Book  Triangles  Polygons  Coordinate Geometry  Factorials  Circles  Number Theory  Remainders; 8. Overlapping Sets  PDF of Math Book; 10. Remainders  GMAT Prep Software Analysis  SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS)  Tricky questions from previous years.
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.
What are GMAT Club Tests? Extrahard Quant Tests with Brilliant Analytics



Intern
Joined: 08 May 2010
Posts: 14

Re: If the letters a, A, b, B, c, and C are arranged at random in a row
[#permalink]
Show Tags
15 Oct 2010, 09:29
Bunnel,
Need your help in understanding this.
If they are asking for the probability of arranging the lower case abc in alphabetical order
I am assuming that first a,b,c and then A , B, C can we be arranged in 3! possible ways.
Desired outcomes = 1 X 3!
Total possible outcomes = 6! as all the 6 letters can be arranged in 6! ways
hence prob = 3! / 6! = 1/120.
Please comment on where I am going wrong?
Thanks!



Manager
Joined: 22 Jun 2010
Posts: 155

Re: If the letters a, A, b, B, c, and C are arranged at random in a row
[#permalink]
Show Tags
15 Oct 2010, 10:29
hey Bunuel what's wrong with my approach? A,a,b,B,c,C desired mode:abc total :6! p=4!/6!



Math Expert
Joined: 02 Sep 2009
Posts: 47200

Re: If the letters a, A, b, B, c, and C are arranged at random in a row
[#permalink]
Show Tags
15 Oct 2010, 12:15
sjgudapa wrote: Bunnel,
Need your help in understanding this.
If they are asking for the probability of arranging the lower case abc in alphabetical order
I am assuming that first a,b,c and then A , B, C can we be arranged in 3! possible ways.
Desired outcomes = 1 X 3!
Total possible outcomes = 6! as all the 6 letters can be arranged in 6! ways
hence prob = 3! / 6! = 1/120.
Please comment on where I am going wrong?
Thanks! imania wrote: hey Bunuel what's wrong with my approach? A,a,b,B,c,C desired mode:abc total :6! p=4!/6! The problem with both solutions above is that favorable outcomes are much more, namely 120. {***}{a}{b}{c}  \(4*3!=24\) (capital letters are together); {**}{a}{*}{b}{c}  \(C^2_3*2*4*3=72\) (2 capital letters are together); {*}{a}{*}{b}{*}{c}  \(C^3_4*3!=24\) (capital letters are separated); \(24+72+24=120\) > \(P=\frac{120}{6!}=\frac{1}{6}\). But this is a long way of solving. Consider one particular arrangement: A*B*C*, lower case letters for *. We can arrange lower case letters instead of * in 3!=6 ways but only one will be in alphabetical order AaBbCc, so 1 out of 6. For other such cases also only one out of 6 will be in alphabetical order (ABCabc, ....), so P=1/6. Basically we can ignore capital letters for this problem and say: 3 letters a, b, and c can be arranged in 3!=6 different ways and only one of them will be in increasing alphabetical order, namely: abc, so P=1/6.
_________________
New to the Math Forum? Please read this: Ultimate GMAT Quantitative Megathread  All You Need for Quant  PLEASE READ AND FOLLOW: 12 Rules for Posting!!! Resources: GMAT Math Book  Triangles  Polygons  Coordinate Geometry  Factorials  Circles  Number Theory  Remainders; 8. Overlapping Sets  PDF of Math Book; 10. Remainders  GMAT Prep Software Analysis  SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS)  Tricky questions from previous years.
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.
What are GMAT Club Tests? Extrahard Quant Tests with Brilliant Analytics



Intern
Joined: 10 Jul 2010
Posts: 36

Re: If the letters a, A, b, B, c, and C are arranged at random in a row
[#permalink]
Show Tags
15 Oct 2010, 21:42
Hi Bunuel,
Even i also think that answer should be 4!/6!



Retired Moderator
Joined: 02 Sep 2010
Posts: 775
Location: London

Re: If the letters a, A, b, B, c, and C are arranged at random in a row
[#permalink]
Show Tags
16 Oct 2010, 00:50
deeplakshya wrote: Hi Bunuel,
Even i also think that answer should be 4!/6! Think of these arrangements as the following : ___[]___[]___[]____ Where [] act as placeholders for the smaller case alphabets. And for each arrangement of small case letters, the ___ are used as placeholders for one of more upper case letters. For Eg. The arrangement of small case letters __b__a__c___ can then produce several final arrangements such as ABCbac or bACaBc etc etc Now all I am going to say is that for each arrangement of type ___b___a___c___ there are an equal number of final arrangements possible. As you just change the small case letters used in your placeholders keeping the upper case ones constant. How many types of arrangement exist ? The number of ways to place small case letters in place holders which is 3! How many of these have a,b,c in order ? Just 1 : __a__b__c__ So probability = 1/6
_________________
Math writeups 1) Algebra101 2) Sequences 3) Set combinatorics 4) 3D geometry
My GMAT story
GMAT Club Premium Membership  big benefits and savings



Manager
Joined: 20 Apr 2010
Posts: 185
Schools: ISB, HEC, Said

Re: If the letters a, A, b, B, c, and C are arranged at random in a row
[#permalink]
Show Tags
16 Oct 2010, 03:54
I am totally confused
Bunuel can you pls simplyfy the answer for me
Thanks in advance..



Math Expert
Joined: 02 Sep 2009
Posts: 47200

Re: If the letters a, A, b, B, c, and C are arranged at random in a row
[#permalink]
Show Tags
17 Oct 2010, 06:32



Intern
Joined: 10 Oct 2010
Posts: 6

Re: If the letters a, A, b, B, c, and C are arranged at random in a row
[#permalink]
Show Tags
17 Oct 2010, 08:27
{**}{a}{*}{b}{c} 2C3*2*4*3=72 (2 capital letters are together); plz explain it



NonHuman User
Joined: 09 Sep 2013
Posts: 7335

Re: If the letters a, A, b, B, c, and C are arranged at random in a row
[#permalink]
Show Tags
01 Oct 2017, 03:25
Hello from the GMAT Club BumpBot! Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up  doing my job. I think you may find it valuable (esp those replies with Kudos). Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________
GMAT Books  GMAT Club Tests  Best Prices on GMAT Courses  GMAT Mobile App  Math Resources  Verbal Resources




Re: If the letters a, A, b, B, c, and C are arranged at random in a row &nbs
[#permalink]
01 Oct 2017, 03:25






