How many words, with or without meaning, each of 2 vowels and 3 consonants can be formed from the letters of the word DAUGHTER?
The word DAUGHTER has 3 vowels A, E, U and 5 consonants D, G, H, T and R.
The three vowels can be chosen in 3C2 as only two vowels are to be chosen.
Similarly, the five consonants can be chosen in5C3 ways.
∴ Number of choosing 2 vowels and 5 consonants would be 3C2 ×
5C3
= 30
∴ Total number of ways of is 30
Each of these 5 letters can be arranged in 5 ways to form different words = 5P5
Total number of words formed would be = 30 × 120 = 3600
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