- 10080
- 4989600
- 120960
- None of these
- None of these
Answer: Option 3
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 = $$\frac{{8!}}{{\left( {2!} \right)\left( {2!} \right)}}$$ = 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 ∴ Required number of words = (10080 x 12) = 120960