Misc 1
How many words, with or without meaning, each of 2 vowels and 3 consonants can be formed from the letters of the word DAUGHTER?
Number ways of selecting 2 vowels & 3 consonants
= 3C2 × 5C3
= 3!/2!(3 − 2)! × 5!/3!(5 − 3)!
= 3!/2!1! × 5!/3!2!
= 30
Now,
Each of these 5 letters can be arranged in 5 ways
Number of arrangements = 5P5
= 5!/(5 − 5)!
= 5!/0!
= 5!
= 5 × 4 × 3 × 2 × 1
= 120
Thus,
Total number of words
= Number of ways of selecting × Number of arrangements
= 30 × 120
= 3600

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 12 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.

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