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.
Vinod said:
1 decade ago
Why divide 7! by 2! ? because you can treat the problem as a permutation with subgroups of identical items. the general formula is nPn1,n2,n3... equals n! divided by n1!n2!n3!...
In this problem you have n = 7 letters (6 plus the vowel group). two letters are the same so n1 = 2. the rest are unique so the 5 other subgroups = 1. so you 7! divided by
2!1!1!1!1!1! . the answer as given simply didn't write out the 1! terms.
In this problem you have n = 7 letters (6 plus the vowel group). two letters are the same so n1 = 2. the rest are unique so the 5 other subgroups = 1. so you 7! divided by
2!1!1!1!1!1! . the answer as given simply didn't write out the 1! terms.
Divya said:
1 decade ago
Good explanation. Thank you.
Suja said:
1 decade ago
We consider all vowels as one letter i.e. OOAIO is a letter + rest of the 6 letters = 1+6 =7.
Raghav said:
1 decade ago
What is process when same letter is come in like as this question?
Thanks.
Thanks.
Kumaran said:
1 decade ago
How the 7 is came instead of 6 (CRPRTN).
Venumadhav said:
1 decade ago
Actually if you consider ooo as o and rr as are the there are 8 distinct alphabets. C O R P A T I N.
Nishtha sharma said:
1 decade ago
Here we can simply separate out the common alphabet.
in CORPORATION , o is 3 times and r is two times, putting together we have,OOORRCPATIN . now the total unique alphabets are 7 and thus the answer is 7%=7*6*5*4*3*2*1= 50400 . the common alphabets dun need any permutation.
in CORPORATION , o is 3 times and r is two times, putting together we have,OOORRCPATIN . now the total unique alphabets are 7 and thus the answer is 7%=7*6*5*4*3*2*1= 50400 . the common alphabets dun need any permutation.
Priyanka said:
1 decade ago
I also can't understand division. Is there any formula ?
Satty said:
1 decade ago
I have the same question, Is there a formula behind ?
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.
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