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.
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?
Ankit said:
1 decade ago
(5!/3!) and (7!/2!) is due to the reason that in the vowels O comes 3 times therefore it has to be in the P&C part too. same case with consonants
Vishnupriya said:
10 years ago
Find the number of ways in which an arrangement of four letter can be made from the letters of PRECIPITATION?
Please help me to solve this problem.
Please help me to solve this problem.
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!
Keerthana said:
9 years ago
But here, R is repeated 2times, in vowels O is repeated 3 times. So we have to consider R & O.
So, 7!/2! & 5!/3! is taken.
So, 7!/2! & 5!/3! is taken.
Kiran said:
1 decade ago
In how many different ways can the letters of the word 'LEADING' be arranged in such a way that the vowels always not together.
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.
Pritesh Patel said:
1 decade ago
Why we dividing 7! and 5! by 2! and 3!, respectively.
Is there any formula for that? What is the Logic Behind it?
Thanks.
Is there any formula for that? What is the Logic Behind it?
Thanks.
Sindhuja said:
1 decade ago
If we have more than one consonants or vowels being repeated again. Then how does the calculation will be?
Eg : Appetite.
Eg : Appetite.
Baz said:
1 decade ago
Good day!
How did you get 2520 and 20 respectively because if u divide 7/2 and 5/3.
You will get this 3.5 and 1.7.
How did you get 2520 and 20 respectively because if u divide 7/2 and 5/3.
You will get this 3.5 and 1.7.
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