In how many ways can the letters of machine be arranged so that the vowels come at odd places

Answer & Explanation

Answer: Option C

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 = $$\frac{8 !}{(2 !) (2 !)}$$ = 10080.

Now, AEAI has 4 Letters in which A occurs 2 times and the rest are different.

Number of ways of arranging these letters = $$\frac{4 !}{2 !}$$ = 12.

$$\therefore$$ Required number of words = (10080 * 12) = 120960.

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