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Register now and save up to $200 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 Thanked: 2 times Target GMAT Score: 780+ #### how many words Mon Sep 08, 2014 4:22 am Elapsed Time: 00:00 • Lap #[LAPCOUNT] ([LAPTIME]) 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 Need free GMAT or MBA advice from an expert? Register for Beat The GMAT now and post your question in these forums! ### GMAT/MBA Expert Jim@StratusPrep MBA Admissions Consultant Joined 11 Nov 2011 Posted: 2278 messages Followed by: 265 members Thanked: 659 times 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.
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### GMAT/MBA Expert

Brent@GMATPrepNow GMAT Instructor
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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
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Check out the online reviews of our course
Come see all of our free resources

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Mon Sep 08, 2014 5:59 am
Oops, was a bit sleepy this morning. Thanks to Brent for the next step.

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-- Daily assignments to fit your exam timeline
-- Organized review that is tailored based on your abiility
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-- 100% Free Trial and less than \$20 per month after.
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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

### GMAT/MBA Expert

Brent@GMATPrepNow GMAT Instructor
Joined
08 Dec 2008
Posted:
10878 messages
Followed by:
1215 members
Thanked:
5207 times
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:
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
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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.

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