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.
Arvind said:
1 decade ago
For @Baz and @Emmanuel .Its not 5/3 its 5!/3! (factorial ways).
The formula for the division of this is give as a result in Important Formulas prescribed in this site (Formula 4). But rather than the formula it is more of Division Logic. This Division logic comes more often in chapters of Prob and statistics.
" Logic - for the vowel letters OOAIO, consider only OOO. In 3 spaces only 1 combination can be made, so in 5 spaces (OOO_ _ )how many combination can be made? hence 5!/3!.
Division is cummulative subtraction ( therefore in 3! ways only 1 way is the right answer and other all 3! - 1 are wrong answers)
The formula for the division of this is give as a result in Important Formulas prescribed in this site (Formula 4). But rather than the formula it is more of Division Logic. This Division logic comes more often in chapters of Prob and statistics.
" Logic - for the vowel letters OOAIO, consider only OOO. In 3 spaces only 1 combination can be made, so in 5 spaces (OOO_ _ )how many combination can be made? hence 5!/3!.
Division is cummulative subtraction ( therefore in 3! ways only 1 way is the right answer and other all 3! - 1 are wrong answers)
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.
Ramya said:
1 decade ago
How you get 2520?
Gerald said:
1 decade ago
Please I'll like to know how you get 2520 and 20?
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.
Hema said:
1 decade ago
How will be7!/2! = 2520?
Raj said:
1 decade ago
Hi friends actually that is a one formula npr formula is used.
Preeti said:
1 decade ago
Which formula is used in 7!/2!?
Kirti said:
1 decade ago
7!/2! = 2520. How is possible?
Ram Mohan said:
1 decade ago
Hi.
In the above {CRPRTN (OOAIO)} (OOAIO can be treated as one letter).
Out of those 7 letters can be arranged in 7! ways. But there are 2 R's is there. They can exchange their places. That's why we are doing 7!/2!.
7! = 7*6*5*4*3*2*1 = 5040/2! = 2520.
In the vowels similarly 3 O's can exchange their places.
5!/3! = 5*4*3*2*1/3*2*1 = 20 ways.
= 2520*20 = 50400.
In the above {CRPRTN (OOAIO)} (OOAIO can be treated as one letter).
Out of those 7 letters can be arranged in 7! ways. But there are 2 R's is there. They can exchange their places. That's why we are doing 7!/2!.
7! = 7*6*5*4*3*2*1 = 5040/2! = 2520.
In the vowels similarly 3 O's can exchange their places.
5!/3! = 5*4*3*2*1/3*2*1 = 20 ways.
= 2520*20 = 50400.
Post your comments here:
Quick links
Quantitative Aptitude
Verbal (English)
Reasoning
Programming
Interview
Placement Papers