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Aptitude - Permutation and Combination - Discussion

@ : Home > Aptitude > Permutation and Combination > General Questions - Discussion

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"Forgiveness is a virtue of the brave."
- Indira Gandhi
2. 

In how many different ways can the letters of the word 'LEADING' be arranged in such a way that the vowels always come together?

[A]. 360[B]. 480
[C]. 720[D]. 5040
[E]. None of these

Answer: Option B

Explanation:

The word 'LEADING' has 7 different letters.

When the vowels EAI are always together, they can be supposed to form one letter.

Then, we have to arrange the letters LNDG (EAI).

Now, 5 (4 + 1 = 5) letters can be arranged in 5! = 120 ways.

The vowels (EAI) can be arranged among themselves in 3! = 6 ways.

Required number of ways = (120 x 6) = 720.


Shoba said: (Sat, Sep 4, 2010 06:31:36 AM)    
 
Other than vowels there are only 4 letter then how it s possible to get 5!.

Sai said: (Fri, Sep 10, 2010 02:26:28 AM)    
 
HI SHOBA,.

4 consonants + set of vowels (i. E. , L+N+D+G+ (EAI) ).

We should arrange all these 5. So we get 5!.

I think you understood.

Sachin Kumar said: (Wed, Sep 29, 2010 08:40:31 AM)    
 
Please make me understand this answer as did not get.

Sri said: (Sun, Oct 10, 2010 09:12:07 AM)    
 
As vowels are together take (EAI) as single letter i.e. , total no of letters are 5 (L, N, D, G, {EAI}).

No of ways can arrange these 5 letters are 5! ways.

Now we arranged 5 letters (L, N, D, G, {EAI}).

Next we have to arrange E, A, I (they may be EAI/EIA/AEI/AIE/IAE/IEA).

All these combinations imply that vowels are together.

So we have to multiply 5! and 3!.

Subbu said: (Thu, Jan 6, 2011 03:09:54 AM)    
 
7!=5040

Madhusudan said: (Mon, Mar 14, 2011 10:00:52 AM)    
 
Could you kindly let me know what is ( ! ).Howe 5! = 120 ?

Sundar said: (Mon, Mar 14, 2011 10:38:38 AM)    
 
@Madhusudan

5! = 5 Factorial = 1 x 2 x 3 x 4 x 5 = 120

Laxmikanth said: (Sat, Mar 26, 2011 11:54:29 PM)    
 
When should we take the one or more letters as a single unit and why?

Moaned said: (Fri, Apr 8, 2011 10:34:06 AM)    
 
I am not getting

Jessie said: (Sun, Apr 10, 2011 05:47:38 AM)    
 
7 letter word = LEADING
CONDITION = VOWELS TO BE TOGETHER, HENCE (EAI) TO FOR A WORD
SO NO. OF WORDS = L,(EAI),D,N,G = 5
permuation to arrange 5 letters = nPr= n!/(n-r)!=5!/0!=5!
0! is assumed to be 1!)
EAI can be arranged among each other in = nPr = 3!/(3-3)= 3!
hence 5! x 3! = 120 x 6 = 720

Mayur said: (Fri, Apr 15, 2011 02:30:58 AM)    
 
How it came like nPr formula and how you have solve it? please let me know.

Bharti said: (Mon, Jul 11, 2011 06:54:15 AM)    
 
Thanks a lot. I had confusion before your explanations. Thanks a lot.

Pavan@9966606261 said: (Fri, Aug 5, 2011 12:14:00 PM)    
 
@mayur.

You just look when ever you open the new exercise there will be availability of basic formulas. If you go through them half of the task would be finished easily. Have a good day buddy.

Siva said: (Sun, Oct 16, 2011 12:36:43 PM)    
 
Permutations and combinations always make me to confuse much.

How to decide based on the descriptive aptitude question ?

Shiva said: (Tue, Oct 18, 2011 08:30:16 PM)    
 
Why we have taken 5 (4 + 1) ?

Santosh Kumar Pradhan said: (Thu, Oct 27, 2011 01:00:33 PM)    
 
Total member 7
out of which 5 consonant and 3 vowels
take 3 vowls as a 1
hen number of consonant will arrange 5! ways
and these 3 vowels will arrange 3! ways
though,5!*3!=720

Bhavik said: (Fri, Nov 4, 2011 11:28:22 AM)    
 
How to read these nPr ?

Sagar Choudhary said: (Sun, Nov 6, 2011 07:02:12 PM)    
 
What is this 5! and 3! ?

A.Vamsi Krishna said: (Mon, Jan 30, 2012 06:18:08 AM)    
 
"!" this implies factorial that means a number is multiplied
like for example take number 5 then its factorial will be
taken as 5*4*3*2*1 and this is equal to 120.

Ncs said: (Thu, Feb 2, 2012 05:55:31 PM)    
 
Why not 5! + 3! ?

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