There are total 9 letters in the word COMMITTEE in which there are 2M's, 2T's, 2E's.

The number of ways in which 9 letters can be arranged = 9 !/( 2!2!2!) = 45360

There are 4 vowels O,I,E,E in the given word. If the four vowels always come together, taking them as one letter we have to arrange 5 + 1 = 6 letters which include 2Ms and 2Ts and this be done in 6 !/(2! × 2!) = 180 ways. In which of 180 ways, the 4 vowels O,I,E,E remaining together can be arranged in 4 !/2 ! = 12 ways.

The number of ways in which the four vowels always come together = 180 x 12 = 2160

No of possible arrangement = 45360 - 2160 = 43200