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# In how many ways can the letters of the word MANIFOLD be arr

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Director
Joined: 07 Mar 2019
Posts: 911
Location: India
GMAT 1: 580 Q43 V27
WE: Sales (Energy and Utilities)
Re: In how many ways can the letters of the word MANIFOLD be arr  [#permalink]

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26 Jan 2020, 06:30
Sorry for jumping in between.
Pritishd
Since we have to keep vowel separated the requirement of 6 spaces arrive. Here's as i understand
A. When Vowels start the word (Positions taken by the vowel)
1 3 5/6/7/8 (4 ways)
1 4 6/7/8 (3 ways)
1 5 7/8 (2 ways)
1 6 8 (1 way)
Total = 10 ways

B. When Consonants start the word (Positions taken by the vowel)
2 4 6/7/8 (3 ways)
2 5 7/8 (2 ways)
2 6 8 (1 way)

3 5 7/8 (2 ways)
3 6 8 (1 way)

4 6 8 (1 way)

Total = 10 ways
G. Total 10 + 10 = 20

Now, since Consonants are always separated number of ways to arrange them = 5!
Number of ways to arrange Vowels = 3!

Required ways of arrangements = 5! * 3! * 20 = 14400

Pritishd wrote:
Archit3110 wrote:
Pritishd
Vowels are to be arranged separated.

Below if you see we have 6 spaces for vowels and total vowels are 3 so possible arrangement for vowels in 6 spaces:6*5*4..

_M_N_D_L_F_

Hope this helps

Hi Archit3110,

I do not understand the part were we consider that there will be 6 spaces to arrange the 3 vowels after the 5 consonants are arranged. Shouldn't there be only 3 spaces after arranging 5 consonants?

IMPORTANT: For each arrangement of 5 consonants, there are 6 spaces where the VOWELS can be placed.
For example, in the arrangement MNDLF, we can add spaces as follows _M_N_D_L_F_

Warm Regards,
Pritishd

Hi Archit3110,

My doubt still remains. I can see that there are 6 spaces but my question was that how did you arrive at those 6 spaces? Once we arrange the 5 consonants will we not have only 3 spaces left? Is this some kind of a method were we assume an available space before and after every element?

Warm Regards,
Pritishd

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GMATPREP1 590(Q48,V23) March 6, 2019
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Re: In how many ways can the letters of the word MANIFOLD be arr   [#permalink] 26 Jan 2020, 06:30

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