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?
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 10 of 10.
Riya said:
1 decade ago
@Tom and @Shantha.
Whenever there is a reference to some arrangement it is permutation. Whenever there is a reference to some selection it is combination.
The given question requires us to find the number of ways in which the word LEADING can be arranged with the condition that the vowels (EAI) always be together. Thus we need to apply the concept of permutation.
Here, since the vowels EAI must always be together we consider it as a single word (EAI).
Thus, LDNG (EAI) make a 5 letter word.
It can be arranged in 5p5 ways = 5!ways.
Now, since EAI can arrange itself in 3p3 or 3! ways, the word LDNG (EAI).
Can thus be arranged or PERMUTED in 3!*5! ways = 720 ways.
Whenever there is a reference to some arrangement it is permutation. Whenever there is a reference to some selection it is combination.
The given question requires us to find the number of ways in which the word LEADING can be arranged with the condition that the vowels (EAI) always be together. Thus we need to apply the concept of permutation.
Here, since the vowels EAI must always be together we consider it as a single word (EAI).
Thus, LDNG (EAI) make a 5 letter word.
It can be arranged in 5p5 ways = 5!ways.
Now, since EAI can arrange itself in 3p3 or 3! ways, the word LDNG (EAI).
Can thus be arranged or PERMUTED in 3!*5! ways = 720 ways.
Tom said:
1 decade ago
In what situations we can permutation or combination?
Shantha said:
1 decade ago
Then how we won't take E+A+I+(LDNG) = 4.
Sagar said:
1 decade ago
Hi friends.
We know that formula n!=n (n-1) (n-2).....3.2.1. Suppose there n way to choose first element (since there are n elements).
After that there are n-1 ways to choose second element because already we choose one element from n elements that's why we are assuming this way. Similarly n-2 ways to chose the third element..etc it's going like this.
n!=n (n-1).
n!=n (n-1) (n-2) if n>2 or equals 2.
n!=n (n-1) (n-2) (n-3) if n>3 or equals 3.
Hope you understood.
We know that formula n!=n (n-1) (n-2).....3.2.1. Suppose there n way to choose first element (since there are n elements).
After that there are n-1 ways to choose second element because already we choose one element from n elements that's why we are assuming this way. Similarly n-2 ways to chose the third element..etc it's going like this.
n!=n (n-1).
n!=n (n-1) (n-2) if n>2 or equals 2.
n!=n (n-1) (n-2) (n-3) if n>3 or equals 3.
Hope you understood.
Ranjeet said:
1 decade ago
Well I am confused. Somewhere n! is done whereas somewhere (n-1)! is used.
Can someone explain about it?
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.
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