In how many different ways can the letters of the word 'MATHEMATICS' be arranged so that the vowels always come together ?	Pick: A) 120960 B) 135650 C) 115850 D) 142560 E) 185260
In the word 'MATHEMATICS' we treat the two vowels AEAI as one letter. Thus,we have MTHMTCS (AEAI)   Now, we have to arranged 8 letters, out of which M occurs twice, T occurs twice and the rest are different.   Number of ways of arranging these letters= 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 =4!/2!=12.   Required number of ways =(10080*12)= 
<gadget id="calculator">(10080*12)</gadget>
<output>120_960</output>
120960.   120960nswer is 120960
<result>A</result>
In how many different ways can the letters of the word 'MATHEMATICS' be arranged so that the vowels always come together ?