Aptitude - Permutation and Combination - Discussion

Discussion Forum : Permutation and Combination - General Questions (Q.No. 2)
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?
360
480
720
5040
None of these
Answer: Option
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.

Video Explanation: https://youtu.be/WCEF3iW3H2c

Discussion:
97 comments Page 8 of 10.

A.Vamsi krishna said:   1 decade ago
"!" 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.

Sagar choudhary said:   1 decade ago
What is this 5! and 3! ?

Bhavik said:   1 decade ago
How to read these nPr ?

Santosh kumar pradhan said:   1 decade ago
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

Shiva said:   1 decade ago
Why we have taken 5 (4 + 1) ?

Siva said:   1 decade ago
Permutations and combinations always make me to confuse much.

How to decide based on the descriptive aptitude question ?

Shrinivas said:   1 decade ago
Hi if two vowels are repeated in same word then will you take it as same or as different?

Brian said:   9 years ago
Correct me if I'm wrong but,

There are 7 letters:

L E A D I N G

3 vowels and 5 non-vowels.

I got the part where we need to permutate 3 and 5, resulting with 3!*5!. But aren't there also several other positions that these vowels could be positioned?

For Example:

AIELDNG is one factor, another factor is LAIEDNG, another factor is LDAIENG.

As you can see, the positions of the 3 vowels with each other are the same, and the order of non-vowels in the word is also the same, but I only changed the position of the starting point for the vowel permutations, starting from the first position, to the second, to the third. So, I believe that the answer should be 3!*5!*5. Since there are 5 different ways you could represent the same order of vowels in different positions with the same order of non-vowels.

Please do correct me if I'm wrong or if I misunderstood the question

Siva said:   9 years ago
Other than vowels there are only 4 letter then how it s possible to get 5!.

Peter said:   9 years ago
If at least two vowels always together then what will be the answer for LEADING ?


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