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.
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)
Usama zaka said:
1 decade ago
@Titesh n Tushar
8! meanx (8*7*6*5*4*3*2*1) which gives us 40320 similarly (2!)(2!) gives us 4. So dividing 40320/4 we get 1008.
Hope you understand.
8! meanx (8*7*6*5*4*3*2*1) which gives us 40320 similarly (2!)(2!) gives us 4. So dividing 40320/4 we get 1008.
Hope you understand.
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.
Deepa said:
1 decade ago
Why dont we use nPr here...as we were using that in last sum. whats the need otherwise where to use nPr..can anybody explain plz ?
Popra Tetseo said:
7 years ago
Anyone can please solve this for me? In how many ways PENCIL be arranged so that P and C are next to each other?
(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.
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
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.
Krishan Senarath said:
8 years ago
If four countries are contesting for 5 cups in a competition, how many results can be there?
Rakesh said:
7 years ago
But here are 6 odd spaces and 4 vowels shouldn't we consider that? Please explain to me.
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