Question

the number of arrangements of the letters of the word MATHS in which the vowel always occupies the middle position is equal to​

Answer 1

• 4So total no of way = 8!*4!/(2!* 2!*2!)

Answer 2

Answer:

Math can be written in 24 distinct ways using just the letters. We will treat the vowels AEAI as a single letter in the word "mathematics." MTHMTCS is the result (AEAI).

Step-by-step explanation:

What is the number of letter arrangements in the word math?

The letters in the word math can be arranged in 24 distinct ways. We have eight letters (M, T, H, M, T, C, S, and one letter created by combining all vowels) if we treat these four vowels as a single letter. M occurs twice, T occurs twice, and the remaining letters are all distinct. The order of these eight letters is $\frac{8 !}{2 ! \times 2 !}$ ways. Consequently, the total number of vowel combinations that are always together. $\frac{8 !}{2 ! \times 2 !} \times \frac{4 !}{2 !}$.

The vowels AEAI are considered to be one letter in the word "mathematics." MTHMTCS is the result (AEAI). Math has the correct spelling. The sound is a short "a." Do it once more. Often, only one vowel letter is used to spell a short vowel sound. Total number of possible arrangements for the letters in the word "Mathematics" is 11!/(2! 2! 2!) ∴ Vowels are retained together 4/165 of the time.

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