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 3 of 4.
Kerese said:
8 years ago
@ALL.
We should notice that in the word "mathematics'", m and t occurred twice 8!/2!2!.
We should notice that in the word "mathematics'", m and t occurred twice 8!/2!2!.
Gouthami said:
7 years ago
My answer is 11!/2!2!2!. Is it is wrong, please explain the answer I have a dought.
Wolanyo said:
1 decade ago
How many ways can we arrange so that the two Ms do not come together?
Srav's said:
8 years ago
I am not getting this answer please sir give me a clear explanation.
Sudama said:
9 years ago
Can we use permutation(nPr) method? & also Used Other Methods.
VAIBHAV said:
1 decade ago
(AEAI) can also have different arrangement like AAEI, AIAE...etc.
Ritesh kumar said:
1 decade ago
Sir I want to know 10080 and 8/(2!) (2!) how comes.
Rachael said:
8 years ago
How can we know that how to separate the vowels?
Rohit Soni said:
10 years ago
Sir, how have you solved 8!/(2!) (2!) and 4!/2!?
Tushar said:
1 decade ago
I want to know 8/(2!) (2!)=10080 how comes.
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