Register    Login    Search    Rss Feeds

Forums Home » Ask An Instructor » GMAT Math » General Math Questions


 Page 1 of 1 [ 5 posts ] 



  Print view Print view Previous topic Previous topic | Next topic Next topic
 

MEDITERRANEAN combinatorics

Author Message
lakita7
 Post subject: MEDITERRANEAN combinatorics
 Post Posted: Tue May 24, 2011 12:30 pm 
Offline
Course Students


Posts: 2
I came across the following problem and struggle to understand how the answer (59) was achieved:

How many different four letter words can be formed (the words need not be meaningful) using the letters of the word "MEDITERRANEAN" such that the first letter is E and the last letter is R?

I am trying to use the following slot method:

1) There are 3 choices for E in the first position, 2 choices for R in the last position, and 11 remaining letters, giving us:
3 x 2 x 11!

2) of the remaining letters, we have 2 E, 2A and 2N where "order doesn't matter", giving us:
(3 x 2 x 11!) / (2! x 2! x 2!)

Which doesn't yield 59... Could you please help me get to the right result utilizing this approach?
Top 
george.kourdin
 Post subject: Re: MEDITERRANEAN combinatorics
 Post Posted: Thu May 26, 2011 9:58 am 
Offline
Course Students


Posts: 98
think the original idea is correct (start with e and r and figure out the middle)

my thinking was that we want different four letter words so the fact that we have 3 choices for E and 2 choices for R is meaningless because a word E1XXR1 is the same as E2XXR2 (where XX=XX) so we don;t want to multiply 2x3. we just want to find the total amount of combinations that could be formed to fill XX

a) XX is actually XY and the two letters are different, having 8 possible letters to choose from we get 56 combos of XY
b) XX is the same letter. there are 3 possible ways this can be done since 3 Ns, 3 A or 3 Es. notice that we dont have 2Rs because we are already using an R...and voila 3+56 =59
Top 
jnelson0612
 Post subject: Re: MEDITERRANEAN combinatorics
 Post Posted: Sat May 28, 2011 3:20 pm 
Offline
ManhattanGMAT Staff


Posts: 1857
Will you please post the original source for this question?

_________________
Jamie Nelson
ManhattanGMAT Instructor
Top 
lakita7
 Post subject: Re: MEDITERRANEAN combinatorics
 Post Posted: Sun May 29, 2011 12:13 am 
Offline
Course Students


Posts: 2
Many thanks George! After spending so much time on it I just realized they are indeed asking for 4 letter words... Unbelievable that my brain somehow omitted that. Says a lot about reading the question well!

Here is the original source:
http://questionbank.4gmat.com/mba_prep_ ... obability/
Top 
jnelson0612
 Post subject: Re: MEDITERRANEAN combinatorics
 Post Posted: Mon May 30, 2011 1:43 am 
Offline
ManhattanGMAT Staff


Posts: 1857
Great, thank you!

_________________
Jamie Nelson
ManhattanGMAT Instructor
Top 
Display posts from previous:  Sort by  
 
 Page 1 of 1 [ 5 posts ] 





Who is online

Users browsing this forum: No registered users and 1 guest

 
 

 
You cannot post new topics in this forum
You cannot reply to topics in this forum
You cannot edit your posts in this forum
You cannot delete your posts in this forum
You cannot post attachments in this forum

Search for:
Jump to: