Question 257455
in the word DAUGHTER there are 3 vowels(A,U,E) and 5 consonants(D,G,H,T,R), and total of 8 letters

there are four odd places --- 1,3,5 and 7

so 3 places are to be selected of the four odd places for the vowels to fill

this can be done in 4c3 ways=4 ways

now the vowels can arrange among themselves in 3! ways=6

now the remaining 5 consonants fill the remaining 5 places and can be arranged in 5! ways=120

so total no. of words that can be formed=4*6*120

=2880 ans