10 Questions 10 Marks 12 Mins
Given: The probability of keeping vowels together has to be determined. Concepts used: Number of ways in which vowels can be together = Number of times 4 vowels in word Mathematics can be put together Calculation: Number of vowels = {A, E, A, I} = 4 Total letters = {M, A, T, H, E, M, A, T, I, C, S} = 11 Number of ways in which 4 vowels can be together = (8 × 4!)/(2!) Number of ways in which all consonants can be arranged = 7!/(2! × 2!) Total number of ways in which letters in word “Mathematics” are arranged = 11!/(2! × 2! × 2!) P (Vowels are together) = Number of ways in which vowels cannot be together/Total number of ways ⇒ P (Vowels are together) = (8 × 4! ×7!)/(2! × 2! × 2!)/(11!)/(2! × 2! × 2!) = 192/(11 × 10 × 9 × 8) = 4/165 ∴ Probability that vowels are kept together is 4/165. India’s #1 Learning Platform Start Complete Exam Preparation
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Discussion :: Permutation and Combination - General Questions (Q.No.13)
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