Example 20 - Chapter 6 Class 11 Permutations and Combinations

Last updated at April 16, 2024 by

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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 14 years. He provides courses for Maths, Science and Computer Science at Teachoo