How many different words can be formed of the letters of the word - Wikitechy https://www.wikitechy.com/interview-questions/tag/how-many-different-words-can-be-formed-of-the-letters-of-the-word/ Interview Questions Mon, 06 Sep 2021 09:46:58 +0000 en-US hourly 1 https://wordpress.org/?v=7.0 https://www.wikitechy.com/interview-questions/wp-content/uploads/2025/10/cropped-wikitechy-icon-32x32.png How many different words can be formed of the letters of the word - Wikitechy https://www.wikitechy.com/interview-questions/tag/how-many-different-words-can-be-formed-of-the-letters-of-the-word/ 32 32 In how many different ways the letters of the word ‘MATHEMATICS’ can be arranged so that the vowels always come together ? https://www.wikitechy.com/interview-questions/permutation-and-combination/in-how-many-different-ways-the-letters-of-the-word-mathematics-can-be-arranged-so-that-the-vowels-always-come-together/ https://www.wikitechy.com/interview-questions/permutation-and-combination/in-how-many-different-ways-the-letters-of-the-word-mathematics-can-be-arranged-so-that-the-vowels-always-come-together/#respond Tue, 17 Aug 2021 20:15:13 +0000 https://www.wikitechy.com/interview-questions/?p=1933

In how many different ways the letters of the word “MATHEMATICS” can be arranged so that the vowels always come together ?

A. 10080

B. 4989600

C. 120960

D. None of these

Answer : C. 120960

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! / (2!)(2!) = 10080.
Now, AEAI has 4 letters in which A occurs 2 times and the rest are different. Number of ways of arranging these letters = 4! / 2! = 12.
Required number of words = (10080 x 12) = 120960.

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