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I am getting A. However, the OA is C. Below is the OE:

Explanation:

Number of ways of selecting (3 consonants out of 7) and (2 vowels out of 4) = (7C3 x 4C2) ={(7 x 6 x 5)x(4 x 3)}/ {(3 x 2 x 1)x(2 x 1)} = 210. Number of groups, each having 3 consonants and 2 vowels = 210.

Each group contains 5 letters.

Number of ways of arranging 5 letters among themselves = 5! = 5 x 4 x 3 x 2 x 1 = 120. Required number of ways = (210 x 120) = 25200.

I don't understand what is need of arranging the 5 letters again, as 7C3*4C2 will do that already. Can someone tell me where I'm going wrong?

Re: Out of 7 consonants and 4 vowels, how many words of 3 consonants and 2
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04 May 2011, 07:40

Using 4 x 3 / (2 x 1) = 6, to select your vowels... just calculated the number of groupings.

Example: a e i o (4 vowels) 6 POSSIBLE GROUPINGS

a e a i a o e i e o i o

If you take the ARRANGEMENT into account, you should have 12 instead of 6.

a e a i a o e i e o i o e a i a o a i e o e o i

But it's best to just get the possible number of grouping first which is 7C3 4C2 = 210. Then we arrange it by multiplying to 5!.. So as to allow consonants and vowels alternating...

Ex.

c d f e i

This will allow c d e i f.. Alternating elements...

Re: Out of 7 consonants and 4 vowels, how many words of 3 consonants and 2
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04 May 2011, 08:16

subhashghosh wrote:

7C3 * 4C2 * 5!

(7 * 6 * 5)/3! * 4!/2!2! * 120

35 * 6 * 120

= 210 * 120

= 25200

I don't understand what is need of arranging the 5 letters again, as 7C3*4C2 will do that already.

7C3*4C2 will select letters, thereafter one has to arrange those.

Uh.. thanks I think I got it now..

Say for example, the first combination is "r t y u i" You can sure arrange it in 5! ways, and since this is a unique combination, alphabets can be arranged in 5! and still form words not contained in any of the other combinations. Thanks for pointing out. great tip!
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Re: Out of 7 consonants and 4 vowels, how many words of 3 consonants and 2
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22 Apr 2018, 06:38

Top Contributor

gmatpapa 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. 42800

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 video on calculating combinations (like 4C2) in your head - see below

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 (= 25,200 ways)

Answer: C

Note: the FCP can be used to solve the MAJORITY of counting questions on the GMAT. So, be sure to learn it.