Find all School-related info fast with the new School-Specific MBA Forum

It is currently 30 Aug 2014, 16:45

Close

GMAT Club Daily Prep

Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track
Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

How many ways can a selection be done of 5 letters out of 5

  Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:
Manager
Manager
User avatar
Status: Still Struggling
Joined: 02 Nov 2010
Posts: 139
Location: India
GMAT Date: 10-15-2011
GPA: 3.71
WE: Information Technology (Computer Software)
Followers: 5

Kudos [?]: 13 [0], given: 8

How many ways can a selection be done of 5 letters out of 5 [#permalink] New post 11 Jul 2011, 22:21
00:00
A
B
C
D
E

Difficulty:

(N/A)

Question Stats:

20% (00:00) correct 80% (01:59) wrong based on 5 sessions
How many ways can a selection be done of 5 letters out of 5 A's, 4B's, 3C's, 2D's and 1 E.

A. 60
B. 75
C. 71
D. 121
E. 221
[Reveal] Spoiler: OA

_________________

Appreciation in KUDOS please!
Knewton Free Test 10/03 - 710 (49/37)
Princeton Free Test 10/08 - 610 (44/31)
Kaplan Test 1- 10/10 - 630
Veritas Prep- 10/11 - 630 (42/37)
MGMAT 1 - 10/12 - 680 (45/34)


Last edited by Bunuel on 07 Feb 2012, 04:20, edited 1 time in total.
Edited the question
Expert Post
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 25207
Followers: 3419

Kudos [?]: 25106 [0], given: 2702

Re: selection be done of 5 letters [#permalink] New post 07 Feb 2012, 04:19
Expert's post
krishnasty wrote:
How many ways can a selection be done of 5 letters out of 5 A's, 4B's, 3C's, 2D's and 1 E.

A. 60
B. 75
C. 71
D. 121
E. 221


Notice that you won't see such question on the GMAT. So, just for fun.

We have the following letters: {AAAAA}, {BBBB}, {CCC}, {DD}, {E}

There are 7 different cases of 5 letter selections possible:

(5) - all letters are alike - 1 way, all A's;

(4, 1) - 4 letters are alike and 1 different - C^1_2*C^1_4=8, where C^1_2 is # of ways to choose which letter provides us with 4 letters from 2 (A or B) and C^1_4 is # of ways to choose 5th letter from 4 letters left;

(3, 2) - 3 letters are alike and other 2 are also alike - C^1_3*C^1_3=9, where C^1_3 is # of ways to choose which letter provides us with 3 letters from 3 (A, B or C) and C^1_3 is # of ways to choose which letter provides us with 2 letters from 3 (for example if we choose A for 3 letters then we can choose from B, C or D for 2 letters);

(3, 1, 1) - 3 letters are alike and other 2 are different - C^1_3*C^2_4=18, where C^1_3 is # of ways to choose which letter provides us with 3 letters from 3 (A, B or C) and C^2_4 is # of ways to choose which 2 letters provides us with one letter each;

(2, 2, 1) - 2 letters are alike, another 2 letters are also alike and 1 is different - C^2_4*C^1_3=18, where C^2_4 is # of ways to choose which 2 letters provides us with 2 letters from 4 (A, B, C or D) and C^1_3 is # of ways to choose which provides us with 5th letter from 3 letters left;

(2, 1, 1, 1) - 2 letters are alike and other 3 are different - - C^1_4*C^3_4=16, where C^1_4 is # of ways to choose which letter provides us with 2 letters from 4 (A, B, C or D) and C^3_4 is # of ways to choose which 3 letters out of 4 provides us with one letter each;

(1, 1, 1, 1, 1) - all letters are distinct - 1 way (A, B, C, D, E).

Total: 1+8+9+18+18+16+1=71.

Answer: C.
_________________

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.


What are GMAT Club Tests?
25 extra-hard Quant Tests

Get the best GMAT Prep Resources with GMAT Club Premium Membership

Current Student
avatar
Joined: 10 Jan 2010
Posts: 193
Location: Germany
Concentration: Strategy, General Management
Schools: IE '15 (M)
GMAT 1: Q V
GPA: 3
WE: Consulting (Telecommunications)
Followers: 2

Kudos [?]: 22 [0], given: 7

GMAT Tests User
Re: How many ways can a selection be done of 5 letters out of 5 [#permalink] New post 07 Feb 2012, 05:50
Even though it would not appear on GMAT, it is still a good questions to tackle. i am always weak with combinations.
Re: How many ways can a selection be done of 5 letters out of 5   [#permalink] 07 Feb 2012, 05:50
    Similar topics Author Replies Last post
Similar
Topics:
3 Experts publish their posts in the topic How many 5 letter combinations can be made from the letters goodyear2013 1 18 Jul 2014, 10:53
3 Experts publish their posts in the topic In how many ways can a person post 5 letters in 4 letter box bagdbmba 6 03 Feb 2013, 05:11
9 Experts publish their posts in the topic In how many ways can 3 letters out of 5 distinct letters A mk87 12 18 Nov 2011, 00:39
How many ways can we select three letters from the letters TeHCM 14 15 Nov 2005, 18:35
In how many ways can 5 men and 5 women be seated in a krishrads 4 02 Jun 2005, 09:58
Display posts from previous: Sort by

How many ways can a selection be done of 5 letters out of 5

  Question banks Downloads My Bookmarks Reviews Important topics  


GMAT Club MBA Forum Home| About| Privacy Policy| Terms and Conditions| GMAT Club Rules| Contact| Sitemap

Powered by phpBB © phpBB Group and phpBB SEO

Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.