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Example 20 - How many words each of 3 vowels and 2 consonants

Example 20 - Chapter 7 Class 11 Permutations and Combinations - Part 2
Example 20 - Chapter 7 Class 11 Permutations and Combinations - Part 3

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Example 20 How many words, with or without meaning, each of 3 vowels and 2 consonants can be formed from the letters of the word INVOLUTE ? Thus, Number ways of selecting 3 vowels & 2 consonants = 4C3 × 4C2 = 4!/3!1! × 4!/2!2! = (4 × 3!)/(3! × 1!) × (4 × 3 × 2 × 1)/(2 × 1 × 2 × 1) = 4 × 6 = 24 We have selected the letters, Now, we have to arrange Number of arrangements of 5 letters Number of arrangements of 5 letters = 5P5 = 5!/(5 − 5)! = 5!/0! = 5!/1 = 5 × 4 × 3 × 2 × 1 = 120 Thus, Total number of words = Number of ways of selecting × Number of arrangements = 24 × 120 = 2880

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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.