In how many ways can the letters of the word "DAUGHTER" be arranged such that no TWO vowels come together

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Dear student
$F i r s t l e t u s a r r a n g e t h e c o n s o n e n t s i n a r o w . T h i s c a n b e d o n e i n^{5} P_{5} = 5! = 120 w a y s C \times C \times C \times C \times C \times N o w, n o t w o v o w e l s a r e t o g e t h e r i f t h e y a r e p u t a t p l a c e s m a r k e d . T h e 3 v o w e l s c a n f i l l u p t h e s e 6 p l a c e s i n^{6} P_{3} = 6 \times 5 \times 4 = 120 w a y s . h e n c e, T h e t o t a l n u m b e r o f w o r d s = 120 \times 120 = 14400$
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