Question

How many words, with or without meaning, each of 2 vowels and 3 consonants can be formed from the letters of the word DAUGHTER?

Answer 1

Given word is DAUGHTER Here, vowels are A, E, U (3 in number) 

Consonant are D, G, H, T, R (5 in number) 

∴ 2 vowels out 3 and 3 consonant out of 5 can be selected in ³C₂ x ⁵C₃ ways and each selection of 2 vowels and 3 consonants can be arranged in ⁵P₅ =5! ways. 

Required number of words = ³C₂ x ⁵C₃ x 5!

= 3 x (5 x 4)/(2 x 1) x 120 = 3600