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Register now and save up to $200 Available with Beat the GMAT members only code • Get 300+ Practice Questions 25 Video lessons and 6 Webinars for FREE Available with Beat the GMAT members only code • Free Veritas GMAT Class Experience Lesson 1 Live Free Available with Beat the GMAT members only code ## how many words tagged by: Brent@GMATPrepNow This topic has 5 expert replies and 1 member reply nahid078 Master | Next Rank: 500 Posts Joined 13 May 2014 Posted: 105 messages Followed by: 1 members Upvotes: 2 Target GMAT Score: 780+ #### how many words Mon Sep 08, 2014 4:22 am Out of 7 consonants and 4 vowels, how many words of 3 consonants and 2 vowels can be formed? A. 210 B. 1050 C. 25200 D. 21400 D. None of these ### GMAT/MBA Expert Brent@GMATPrepNow GMAT Instructor Joined 08 Dec 2008 Posted: 11283 messages Followed by: 1225 members Upvotes: 5254 GMAT Score: 770 Mon Jul 04, 2016 9:17 am osama_salah wrote: Why did we assume that a letter can not be repeated? e.g. out of B,C,D,F,G,H,J and A,E,I,O we can get: BACAD and ECCEF Good point. The question could be written to be less ambiguous. In fact, we don't even know that the original 7 consonants and 4 vowels are all different. The 11 letters could just be B,B,B,B,B,B,B,A,A,A,A Cheers, Brent _________________ Brent Hanneson â€“ Founder of GMATPrepNow.com Use our video course along with Check out the online reviews of our course Come see all of our free resources GMAT Prep Now's comprehensive video course can be used in conjunction with Beat The GMATâ€™s FREE 60-Day Study Guide and reach your target score in 2 months! ### GMAT/MBA Expert Matt@VeritasPrep GMAT Instructor Joined 12 Sep 2012 Posted: 2640 messages Followed by: 113 members Upvotes: 625 Target GMAT Score: V51 GMAT Score: 780 Thu Jul 07, 2016 3:50 pm osama_salah wrote: Why did we assume that a letter can not be repeated? Great question: I suppose because the answer we'd get if we DIDN'T make that assumption isn't one of the options. That said, (E) would fit, so it's a poorly written Q. I'm guessing it's from the CAT (a rival to the GMAT), on which I've seen other poorly written Qs, but I can't say for sure. Enroll in a Veritas Prep GMAT class completely for FREE. Wondering if a GMAT course is right for you? Attend the first class session of an actual GMAT course, either in-person or live online, and see for yourself why so many students choose to work with Veritas Prep. Find a class now! ### GMAT/MBA Expert Jim@StratusPrep MBA Admissions Consultant Joined 11 Nov 2011 Posted: 2278 messages Followed by: 265 members Upvotes: 660 GMAT Score: 770 Mon Sep 08, 2014 4:57 am This is 7 choose 3 multiplied by 4 choose 2. n!/(n-k)!k! 7 choose 3 = 7!/4!3! = 35 4 choose 2 = 4!/2!2! = 6 35 x 6 = 210 _________________ GMAT Answers provides a world class adaptive learning platform. -- Push button course navigation to simplify planning -- Daily assignments to fit your exam timeline -- Organized review that is tailored based on your abiility -- 1,000s of unique GMAT questions -- 100s of handwritten 'digital flip books' for OG questions -- 100% Free Trial and less than$20 per month after.
-- Free GMAT Quantitative Review

### GMAT/MBA Expert

Brent@GMATPrepNow GMAT Instructor
Joined
08 Dec 2008
Posted:
11283 messages
Followed by:
1225 members
5254
GMAT Score:
770
Mon Sep 08, 2014 5:22 am
nahid078 wrote:
Out of 7 consonants and 4 vowels, how many words of 3 consonants and 2 vowels can be formed?

A. 210
B. 1050
C. 25200
D. 21400
E. None of these
Take the task of creating 5-letter words and break it into stages.

Stage 1: Select the 3 consonants to work with
Since the order in which we select the consonants does not matter, we can use combinations.
We can select 3 consonants from 7 consonants in 7C3 ways (= 35 ways)

Stage 2: Select the 2 vowels to work with
Since the order in which we select the vowels does not matter, we can use combinations.
We can select 2 vowels from 4 vowels in 4C2 ways (= 6 ways)

If anyone is interested, we have a free video on calculating combinations (like 4C2) in your head: http://www.gmatprepnow.com/module/gmat-counting?id=789

Stage 3: Take the 5 selected letters and arrange them.
We can complete this stage in 5! ways (= 120 ways).

By the Fundamental Counting Principle (FCP), we can complete all 3 stages (and thus create all 5-letter words) in (35)(6)(120) ways (= 25200 ways)

--------------------------

Note: the FCP can be used to solve the MAJORITY of counting questions on the GMAT. For more information about the FCP, watch our free video: http://www.gmatprepnow.com/module/gmat-counting?id=775

Then you can try solving the following questions:

EASY
- http://www.beatthegmat.com/counting-problem-company-recruitment-t244302.html
- http://www.beatthegmat.com/picking-a-5-digit-code-with-an-odd-middle-digit-t273110.html
- http://www.beatthegmat.com/permutation-combination-simple-one-t257412.html
- http://www.beatthegmat.com/simple-one-t270061.html
- http://www.beatthegmat.com/mouse-pellets-t274303.html

MEDIUM
- http://www.beatthegmat.com/combinatorics-solution-explanation-t273194.html
- http://www.beatthegmat.com/arabian-horses-good-one-t150703.html
- http://www.beatthegmat.com/sub-sets-probability-t273337.html
- http://www.beatthegmat.com/combinatorics-problem-t273180.html
- http://www.beatthegmat.com/digits-numbers-t270127.html
- http://www.beatthegmat.com/doubt-on-separator-method-t271047.html
- http://www.beatthegmat.com/combinatorics-problem-t267079.html

DIFFICULT
- http://www.beatthegmat.com/wonderful-p-c-ques-t271001.html
- http://www.beatthegmat.com/ps-counting-t273659.html
- http://www.beatthegmat.com/permutation-and-combination-t273915.html

Cheers,
Brent

_________________
Brent Hanneson â€“ Founder of GMATPrepNow.com
Use our video course along with

Check out the online reviews of our course
Come see all of our free resources

GMAT Prep Now's comprehensive video course can be used in conjunction with Beat The GMATâ€™s FREE 60-Day Study Guide and reach your target score in 2 months!

### GMAT/MBA Expert

Joined
11 Nov 2011
Posted:
2278 messages
Followed by:
265 members
660
GMAT Score:
770
Mon Sep 08, 2014 5:59 am
Oops, was a bit sleepy this morning. Thanks to Brent for the next step.

_________________
-- Push button course navigation to simplify planning
-- Daily assignments to fit your exam timeline
-- Organized review that is tailored based on your abiility
-- 1,000s of unique GMAT questions
-- 100s of handwritten 'digital flip books' for OG questions
-- 100% Free Trial and less than \$20 per month after.
-- Free GMAT Quantitative Review

osama_salah Newbie | Next Rank: 10 Posts
Joined
15 Jun 2016
Posted:
8 messages
Mon Jul 04, 2016 7:56 am
Why did we assume that a letter can not be repeated?
e.g. out of B,C,D,F,G,H,J and A,E,I,O we can get:

Brent@GMATPrepNow wrote:
nahid078 wrote:
Out of 7 consonants and 4 vowels, how many words of 3 consonants and 2 vowels can be formed?

A. 210
B. 1050
C. 25200
D. 21400
E. None of these
Take the task of creating 5-letter words and break it into stages.

Stage 1: Select the 3 consonants to work with
Since the order in which we select the consonants does not matter, we can use combinations.
We can select 3 consonants from 7 consonants in 7C3 ways (= 35 ways)

Stage 2: Select the 2 vowels to work with
Since the order in which we select the vowels does not matter, we can use combinations.
We can select 2 vowels from 4 vowels in 4C2 ways (= 6 ways)

If anyone is interested, we have a free video on calculating combinations (like 4C2) in your head: http://www.gmatprepnow.com/module/gmat-counting?id=789

Stage 3: Take the 5 selected letters and arrange them.
We can complete this stage in 5! ways (= 120 ways).

By the Fundamental Counting Principle (FCP), we can complete all 3 stages (and thus create all 5-letter words) in (35)(6)(120) ways (= 25200 ways)

--------------------------

Note: the FCP can be used to solve the MAJORITY of counting questions on the GMAT. For more information about the FCP, watch our free video: http://www.gmatprepnow.com/module/gmat-counting?id=775

Then you can try solving the following questions:

EASY
- http://www.beatthegmat.com/counting-problem-company-recruitment-t244302.html
- http://www.beatthegmat.com/picking-a-5-digit-code-with-an-odd-middle-digit-t273110.html
- http://www.beatthegmat.com/permutation-combination-simple-one-t257412.html
- http://www.beatthegmat.com/simple-one-t270061.html
- http://www.beatthegmat.com/mouse-pellets-t274303.html

MEDIUM
- http://www.beatthegmat.com/combinatorics-solution-explanation-t273194.html
- http://www.beatthegmat.com/arabian-horses-good-one-t150703.html
- http://www.beatthegmat.com/sub-sets-probability-t273337.html
- http://www.beatthegmat.com/combinatorics-problem-t273180.html
- http://www.beatthegmat.com/digits-numbers-t270127.html
- http://www.beatthegmat.com/doubt-on-separator-method-t271047.html
- http://www.beatthegmat.com/combinatorics-problem-t267079.html

DIFFICULT
- http://www.beatthegmat.com/wonderful-p-c-ques-t271001.html
- http://www.beatthegmat.com/ps-counting-t273659.html
- http://www.beatthegmat.com/permutation-and-combination-t273915.html

Cheers,
Brent

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