Aptitude - Permutation and Combination - Discussion
Discussion Forum : Permutation and Combination - General Questions (Q.No. 3)
3.
In how many different ways can the letters of the word 'CORPORATION' be arranged so that the vowels always come together?
Answer: Option
Explanation:
In the word 'CORPORATION', we treat the vowels OOAIO as one letter.
Thus, we have CRPRTN (OOAIO).
This has 7 (6 + 1) letters of which R occurs 2 times and the rest are different.
| Number of ways arranging these letters = | 7! | = 2520. |
| 2! |
Now, 5 vowels in which O occurs 3 times and the rest are different, can be arranged
| in | 5! | = 20 ways. |
| 3! |
Required number of ways = (2520 x 20) = 50400.
Video Explanation: https://youtu.be/o3fwMoB0duw
Discussion:
60 comments Page 6 of 6.
Madhu said:
8 years ago
Why the answers 2520 and 20 are multiplied why not they added?
Please give me the answer.
Please give me the answer.
(4)
Shibu said:
8 years ago
Hi @Madhu.
From the formula, we get only the multiplication so we are doing the same.
From the formula, we get only the multiplication so we are doing the same.
(2)
Raghvendra Patel said:
8 years ago
Should it not be 5!/3! * 6!/2!* 2!.
As first arrange vowel and then consonant separately and then arrange these two packets.
As first arrange vowel and then consonant separately and then arrange these two packets.
Lokesh said:
8 years ago
Yes, there is a logic.
The word corporation 'r' can be repeated two times so it is 2!
And in vowels 'o' can be repeated three times.
So it is 3!
The word corporation 'r' can be repeated two times so it is 2!
And in vowels 'o' can be repeated three times.
So it is 3!
Aswathy said:
7 years ago
Thank you for the given explanation.
(1)
Pavi said:
7 years ago
I am not getting. Can anyone help me to solve this?
(2)
Veera manikantha said:
7 years ago
In CORPORATION their vowels have to be together, so it becomes CRPRTN (OOAIO).
In this, a number of ways is 7!÷2! since R is repeated 2 times and in the vowels, there are 5!÷3! A number of ways. So total number of ways is (7!÷2!) * (5!÷3!)=50400.
In this, a number of ways is 7!÷2! since R is repeated 2 times and in the vowels, there are 5!÷3! A number of ways. So total number of ways is (7!÷2!) * (5!÷3!)=50400.
(4)
Mayuresh Hedau said:
6 years ago
Firstly there are 11 words(5 vowels and 6 non vowels).
Consider 5 vowels =1 and remaining words are 6.
Add them (6+1=7).
In those 7 words count the Repeating words and divide to 7 (likewise 7fact÷2fct) and,
In those 5 vowels count the repeating words to and divide to 5 (5fact÷3 fact).
Multiply both of them :
(7fact÷2fact) * (5fact÷3fact).
= 50400.
Consider 5 vowels =1 and remaining words are 6.
Add them (6+1=7).
In those 7 words count the Repeating words and divide to 7 (likewise 7fact÷2fct) and,
In those 5 vowels count the repeating words to and divide to 5 (5fact÷3 fact).
Multiply both of them :
(7fact÷2fact) * (5fact÷3fact).
= 50400.
(8)
BHAGYESH said:
6 years ago
Thus, we have CRPRTN (OOAIO).
This has 7 (6 + 1) letters of which R occurs 2 times and the rest are different.
The number of ways of arranging these letters = 7!/2! = 2520.
Now, 5 vowels in which O occurs 3 times and the rest are different, can be arranged
In 5!/3! = 20 ways.
This has 7 (6 + 1) letters of which R occurs 2 times and the rest are different.
The number of ways of arranging these letters = 7!/2! = 2520.
Now, 5 vowels in which O occurs 3 times and the rest are different, can be arranged
In 5!/3! = 20 ways.
(7)
Rubbal said:
5 years ago
Thanks all for explaining.
(4)
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