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:
98 comments Page 7 of 10.
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.
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.
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!.
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!.
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