Total no. of letters in the word DAUGHTER = 8, No. of vowels in the word (A, U, E) = 3 No. of consonants in the word (D, G, H, T, R) = 5 So, words can be formed with 2 vowels & 3 consonants in $\binom{3}{2} \times \binom{5}{3}$ ways. ∴ Required no. of words = ${}^{5}P_{5} \times \binom{3}{2} \times \binom{5}{3}$ = $\frac{5!}{0!} \times \frac{3!}{2!\,1!} \times \frac{5!}{3!\,2!}$ = $\frac{5 \times 4 \times 3 \times 2 \times 5 \times 4 \times 3 \times 2}{2 \times 2}$ = 3600