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 3 of 6.
Chandu said:
9 years ago
I understood. Thank you all.
Sofia said:
9 years ago
Where did '7' came from?
Rahul Jha said:
9 years ago
@Sofia.
We have to consider all the vowels as 1 vowel + rest 6 consonants = 7.
We have to consider all the vowels as 1 vowel + rest 6 consonants = 7.
Neethu said:
9 years ago
CORPORATION Vowels Come Together.
Consonants CRPRTN ( R repeat twice).
Vowels OOAIO ( O repeat thrice )
We take 7!/2! * 5!/3!.
Note: 7! means the number of consonants + the vowels taken as "one".
that means 6 + 1 ( CRPRTN + ( OOAIO)).
7!/2! means R repeated twice, so we take 2!.
5!/3! means O repeated thrice, so we take 3! too.
Consonants CRPRTN ( R repeat twice).
Vowels OOAIO ( O repeat thrice )
We take 7!/2! * 5!/3!.
Note: 7! means the number of consonants + the vowels taken as "one".
that means 6 + 1 ( CRPRTN + ( OOAIO)).
7!/2! means R repeated twice, so we take 2!.
5!/3! means O repeated thrice, so we take 3! too.
Maurice said:
9 years ago
Please one should help me out with this complicating question:
(a) How many four and five digits numbers can be formed using 2, 3, 4, 5, 6?
(b) How many will be greater than 5,000?
(c) How many will be odd numbers?
(d) How many will be even numbers?
PLEASE show workings thank you.
(a) How many four and five digits numbers can be formed using 2, 3, 4, 5, 6?
(b) How many will be greater than 5,000?
(c) How many will be odd numbers?
(d) How many will be even numbers?
PLEASE show workings thank you.
Gbenga Felix said:
8 years ago
A school principal and his wife, as well as three other tutors are to be seated in a row so that the principal and his wife are next to each other. Find the total number of ways this can be done.
Please give me the answer.
Please give me the answer.
Naveen said:
8 years ago
@Gbenga.
Total there are 5members while 2are always together so considering 2members as -unit arrangement can be done in 4! Ways and they themselves i.e the principle and wife can be arranged in 2! ways so total no of ways will be 4!*2! = 48ways.
Total there are 5members while 2are always together so considering 2members as -unit arrangement can be done in 4! Ways and they themselves i.e the principle and wife can be arranged in 2! ways so total no of ways will be 4!*2! = 48ways.
Shobhit said:
8 years ago
@Maurice.
a. 5 digit number can be arranged in 5! Ways
4 digit number can be arranged in 5c4 * 4! Ways.
a. 5 digit number can be arranged in 5! Ways
4 digit number can be arranged in 5c4 * 4! Ways.
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!
Post your comments here:
Quick links
Quantitative Aptitude
Verbal (English)
Reasoning
Programming
Interview
Placement Papers