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 1 of 6.
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)
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)
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)
Pavi said:
7 years ago
I am not getting. Can anyone help me to solve this?
(2)
Aswathy said:
7 years ago
Thank you for the given explanation.
(1)
Rajmachawal said:
1 decade ago
Shouldn't there be a multiplication by 2fac in the end because there can be vowels first and then consonants or the consonants first and vowels second?
Arun kumar said:
10 years ago
Which explanation is correct?
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