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:
37 comments Page 2 of 4.
Rachael said:
8 years ago
How can we know that how to separate the vowels?
Krishan Senarath said:
8 years ago
If four countries are contesting for 5 cups in a competition, how many results can be there?
Shree said:
8 years ago
Thanks all for the clear explanations.
Dev said:
2 months ago
But can't the letter AAEI and MMTHCS be arranged within itself. So this increases the combinations.
Chandan said:
8 years ago
In the above solution as suggested in the answer section, we are just taking the 4 vowels set at last, but its not said in the question that the vowels set to come together and at last of the word. The words can also be formed as M (AEAI) THMTCS or more which is not considered.
Rakesh said:
8 years ago
But here are 6 odd spaces and 4 vowels shouldn't we consider that? Please explain to me.
Maswoad said:
7 years ago
@Popra.
In the arrangement of letters of word PENCIL, P and C next to each other means P and C always come together and only one possible arrangement of P and C letter that is PC, CP is wrong. Now think of available letters E, N, I, L, [PC].
So possible arrangement = 5! => 120.
In the arrangement of letters of word PENCIL, P and C next to each other means P and C always come together and only one possible arrangement of P and C letter that is PC, CP is wrong. Now think of available letters E, N, I, L, [PC].
So possible arrangement = 5! => 120.
Sourabh sharma said:
6 years ago
Sir how to find the total arrangements of word ;mathematics, of both A and both M together
AA. MM
AA. MM
Arti said:
2 decades ago
How we consider 8 letter?
Wolanyo said:
1 decade ago
How many ways can we arrange so that the two Ms do not come together?
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