GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 15 Nov 2019, 15:44

### 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

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

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

Author Message
TAGS:

### Hide Tags

Manager
Status: Still Struggling
Joined: 03 Nov 2010
Posts: 111
Location: India
GMAT Date: 10-15-2011
GPA: 3.71
WE: Information Technology (Computer Software)
How many ways can a selection be done of 5 letters out of 5  [#permalink]

### Show Tags

Updated on: 07 Feb 2012, 05:20
00:00

Difficulty:

(N/A)

Question Stats:

23% (00:00) correct 77% (02:41) wrong based on 15 sessions

### HideShow timer Statistics

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

_________________
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)

Originally posted by krishnasty on 11 Jul 2011, 23:21.
Last edited by Bunuel on 07 Feb 2012, 05:20, edited 1 time in total.
Edited the question
Math Expert
Joined: 02 Sep 2009
Posts: 59075
Re: selection be done of 5 letters  [#permalink]

### Show Tags

07 Feb 2012, 05:19
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.

_________________
Manager
Joined: 10 Jan 2010
Posts: 137
Location: Germany
Concentration: Strategy, General Management
Schools: IE '15 (M)
GPA: 3
WE: Consulting (Telecommunications)
Re: How many ways can a selection be done of 5 letters out of 5  [#permalink]

### Show Tags

07 Feb 2012, 06:50
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, 06:50
Display posts from previous: Sort by