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  • How many ways can the letters of the word "MATHEMATICS" be arranged such that all the vowels are in 2nd and 3rd position?Option: 1 9,32,568

How many ways can the letters of the word "MATHEMATICS" be arranged such that all the vowels are in 2nd and 3rd position?

Option: 1

9,32,568


Option: 2

66,08,965


Option: 3

55,87,896


Option: 4

43,54,560


Answers (1)

best_answer

To calculate the number of ways the letters of the word "MATHEMATICS" can be arranged such that all the vowels are in the 2nd and 3rd positions, we need to consider the following:

The word "MATHEMATICS" has 11 letters, including 4 vowels (A, E, A, I) and 7 consonants (M, T, H, M, T, C, S).

First, we fix the two vowel positions (2nd and 3rd). There are 4 vowels to choose from for the 2nd position and 3 vowels remaining for the 3rd position .

Next, we arrange the remaining 9 letters (7 consonants + 2 remaining vowels) in the remaining 9 positions.

The number of ways to arrange the vowels in the 2nd and 3rd positions is 4\times 3= 12.

The number of ways to arrange the remaining 9 letters is 9!.

Therefore, the total number of ways to arrange the letters of the word "MATHEMATICS" such that all the vowels are in the 2nd and 3rd positions is 12 \times 9 !=12 \times 362,880=43,54,560.

Hence, there are 43,54,560 distinct ways to arrange the letters of the word "MATHEMATICS" under the given condition.

 

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