How many different ways can the letters in the word "MATHEMATICS" be arranged so that the vowels always meet?
A. 10080
B. 4989600
C. 120960
D. None of these
Answer:C
How many different ways can the letters in the word "MATHEMATICS" be arranged so that the vowels always meet?
A. 10080 B. 4989600 C. 120960 D. None of these
Explanation: The vowels AEAI are treated as one letter in the word 'MATHEMATICS.'As a result, we have MTHMTCS (AEAI).Now we must arrange eight letters, with M appearing twice, T appearing twice, and the remainder being unique.The number of different ways to arrange these letters is 8!/ (2!)(2!) = 10080.AEAI now contains four letters, with A appearing twice and the rest being unique.The number of different ways to arrange these letters is 4!/2! = 12.(10080 x 12) = 120960 is the required number of words.