Q. 14.3( 94 Votes )

# 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 :

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 ^{3}C_{2} as only two vowels are to be chosen.

Similarly, the five consonants can be chosen in^{5}C_{3} ways.

∴ Number of choosing 2 vowels and 5 consonants would be ^{3}C_{2} ×^{5}C_{3}

= 30

∴ Total number of ways of is 30

Each of these 5 letters can be arranged in 5 ways to form different words = ^{5}P_{5}

Total number of words formed would be = 30 × 120 = 3600

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