Misc 6 - The English alphabet has 5 vowels and 21 consonants

Misc 6 - Chapter 7 Class 11 Permutations and Combinations - Part 2
Misc 6 - Chapter 7 Class 11 Permutations and Combinations - Part 3

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Misc 6 The English alphabet has 5 vowels and 21 consonants. How many words with two different vowels and 2 different consonants can be formed from the alphabet? Number ways of selecting 2 vowels & 2consonants = 5C2 × 21C2 = 5!/(2!(5 − 2)!) × 21!/(2!(21 − 2)!) = 5!/2!3! × 21!/2!19! = (5 × 4 × 3!)/(2 × 1 × 3!) × (21 × 20 × 19!)/(2 × 1 × 19!) = 10 × 210 = 2100 Hence, Total number of ways of selecting 2 vowels and 2 consonants = 2100 We have selected the letters, Now, we have to arrange Number of arrangements of 4 letters Number of arrangements of 4 letters = 4P4 = 4!/(4 − 4)! = 4!/0! = 4!/1 = 4 × 3 × 2 × 1 = 24 ways Thus, Total number of words = Number of ways of selecting × Number of arrangements = 2100 × 24 = 50400

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Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 13 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.