Aptitude - Permutation and Combination - Discussion
Discussion Forum : Permutation and Combination - General Questions (Q.No. 13)
13.
In how many different ways can the letters of the word 'MATHEMATICS' be arranged so that the vowels always come together?
Answer: Option
Explanation:
In the word 'MATHEMATICS', we treat the vowels AEAI as one letter.
Thus, we have MTHMTCS (AEAI).
Now, we have to arrange 8 letters, out of which M occurs twice, T occurs twice and the rest are different.
 Number of ways of arranging these letters = |
8! | = 10080. |
| (2!)(2!) |
Now, AEAI has 4 letters in which A occurs 2 times and the rest are different.
| Number of ways of arranging these letters = | 4! | = 12. |
| 2! |
Required number of words = (10080 x 12) = 120960.
Discussion:
36 comments Page 2 of 4.
Ram Naik said:
1 decade ago
@Wolanyo.
To find out the number of ways to arrange the so that two Ms do not come together.!
Two Ms don't come to gether = Total number of ways - two Ms come together.
Total number ways of arranging MATHEMATICS letters = 11!/(2!*2!*2!) = 4989600.
Two Ms come together = 10!/(2!*2!) = 907200.
Two Ms don't come together = 4989600-907200 = 4082400.
To find out the number of ways to arrange the so that two Ms do not come together.!
Two Ms don't come to gether = Total number of ways - two Ms come together.
Total number ways of arranging MATHEMATICS letters = 11!/(2!*2!*2!) = 4989600.
Two Ms come together = 10!/(2!*2!) = 907200.
Two Ms don't come together = 4989600-907200 = 4082400.
Deepa said:
1 decade ago
Number of ways of arranging these letters = 4!/2! = 2!
And than the answer was = 10080*2*1 = 20160.
And than the answer was = 10080*2*1 = 20160.
Salman khan said:
1 decade ago
Can we use permutation(nPr) method?
VAIBHAV said:
1 decade ago
(AEAI) can also have different arrangement like AAEI, AIAE...etc.
Raji said:
1 decade ago
Why don't take 7c4 instead of 7p4?
Rohit Soni said:
10 years ago
Sir, how have you solved 8!/(2!) (2!) and 4!/2!?
Pruthvi said:
10 years ago
This answer is wrong we have to multiply by 2 at last which indicates arrange of vowel and other group.
Sudama said:
9 years ago
Can we use permutation(nPr) method? & also Used Other Methods.
Baskar said:
9 years ago
In the word 'MATHEMATICS', we treat the vowels AEAI as one letter.
Thus, we have MTHMTCS (AEAI).
7! * 4! => 5040 * 24 => 120960.
Make it simple!
Thus, we have MTHMTCS (AEAI).
7! * 4! => 5040 * 24 => 120960.
Make it simple!
(1)
Pranjali said:
9 years ago
Don't you think the overall answer should be multiplied by 2? MTHMTCS (AEAI) and (AEAI) MTHMTCS. I am little confused here. Anyone help me to get this.
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