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 7 of 10.

Ranjeet said:   1 decade ago
Well I am confused. Somewhere n! is done whereas somewhere (n-1)! is used.

Can someone explain about it?

Samson said:   1 decade ago
God bless you all for your contribution especially you @Jessie for using the formula to break it down well.

Baidyanath jena said:   1 decade ago
When it comes to persons it should be combination.

Pema said:   1 decade ago
When it comes the question for arrangements, then it is a Permutation Or you all can remember it as keyword "PA" P=permutation and A=arrangement.

Likewise, for combination, it is all for selection purpose, remember keyword as "CS" c=combination,s=selection. Then apply formula for each. Easy.

Jhansi sri said:   1 decade ago
Please help me quickly why we take 5!*3!, Why we can't take 5!+3!.

Amnafida said:   1 decade ago
Describe that how we know about here permutation is use?

Amna fida said:   1 decade ago
How we know that factorial will use here?

Taku mambo bellnuisemarbel said:   1 decade ago
Please help me with this; whenever I hear of probability that a variable is being selected what should I think of?

Chithra said:   1 decade ago
As we known very well that * is consider to be AND, + is consider to be OR. Consider the 1st example 7 men and 6 women problem we taken as (7c3*6c2) + (7c4*6c2) + (7c5).

We can also said this as (7c3 AND 6c2) OR (7c4 AND 6c2) OR (7c5).

CONDITION -> 5 people need to select. We should take 3 men from 7 men and 2 women from 6 women or other option is to take 4 men from 7 men and 1 women from 6 women.

That's why we are using * at the place of AND, + at the place of OR. Similarly, we need to consider both the consonant AND vowel not consonant OR vowel.

So we use 5!*3!.

Sanjay(9776387850) said:   1 decade ago
Hi Guys, at first I tell you how can you know is this permutation or combination. Permutation means arrange(row/column) and Combination means selection(group).

i.e. Number and Word are perm. Playing 11 and committee are combi. This is a word so this is perm. You should know the formula that m different objects are alike and n different object are alike if we arrange all the m+n objects such that n objects are always together=(m+1)!*n!

Here n = Vowel = 3 and m = Con. = 4.

So = (4+1)!*3! = 5!*3!.

= 120*6 = 720.


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