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

The word DAUGHTER consists of 3 vowels and 5 consonants

2 vowels and 3 consonants may be selected in ³C₂×⁵C₃ ways

⇒³C₁×⁵C₂ ways

⇒3/1×5×4/1×2

⇒30 ways

5 letters can be arranged in 5! ways or in 5×4×3×2×1

⇒120 ways

∴ Number of words formed by 2 vowels and 3 consonants which are selected from the word DAUGHTER

⇒30×120

⇒3600