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.
Rakesh said:
7 years ago
But here are 6 odd spaces and 4 vowels shouldn't we consider that? Please explain to me.
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)
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.
Prashanth D said:
6 years ago
GIVEN WORD = M A T H E M A T I C S = TOTAL = 11.
Solution:-
VOWEL FROM THE WORD = A A E I -------------------------> (1)
REMAINING LETTERS IN THE WORD = M T H M T C S ------->(2)
CONSIDER [ A A E I ] M T H M T C S = 1 + 7 = 8! divided by 2! 2! [becus we have M M and T T].
FROM ------->A A E I we get 4! and divided 2! [becus we have two A A].
8! 4! DIVIDED BY 2! 2! 2! =======> 120960.
Solution:-
VOWEL FROM THE WORD = A A E I -------------------------> (1)
REMAINING LETTERS IN THE WORD = M T H M T C S ------->(2)
CONSIDER [ A A E I ] M T H M T C S = 1 + 7 = 8! divided by 2! 2! [becus we have M M and T T].
FROM ------->A A E I we get 4! and divided 2! [becus we have two A A].
8! 4! DIVIDED BY 2! 2! 2! =======> 120960.
(5)
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
Sabya said:
7 months ago
Yeah, it is correct but there is a simpler way to do this;
Out of 11 places, the last 4 take it as vowels so there would be 4! places and the remaining 7 places will come together as 7! ways.
Hence, 7!*4!=120960 (that's the answer).
Out of 11 places, the last 4 take it as vowels so there would be 4! places and the remaining 7 places will come together as 7! ways.
Hence, 7!*4!=120960 (that's the answer).
(4)
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