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 4 of 4.
Shree said:
7 years ago
Thanks all for the clear explanations.
Himanshu said:
8 years ago
If vowels never come together then?
Salman khan said:
1 decade ago
Can we use permutation(nPr) method?
Raji said:
1 decade ago
Why don't take 7c4 instead of 7p4?
Riddhi said:
1 decade ago
can't we take it as 7p7*4p4.....
Arti said:
2 decades ago
How we consider 8 letter?
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