How many arrangements are there of the word MATHEMATICS if vowels occur together?
In word, “MATHEMATICS”, find the probability of keeping vowels together.
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Answer (Detailed Solution Below)Option 3 : 4/165 Free Fractions (In trend most asked questions) 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. Last updated on Nov 24, 2022 The Tata Consultancy Service (TCS) had released the date of the TCS National Qualifier Test (NQT). The exam was 15th August 2022. The UG/PG students of B.E./B.Tech/M.E./M.Tech/MCA/M.Sc from the Year of Passing 2023 are going to appear for the NQT. After clearing the National Qualifier Test, the qualified candidates will call for the Interview round. Candidates going to appear for the test can refer to the TCS Previous Year Papers to analyze the level and questions for the exam and improve their preparation.
Post your comments here:Name *: Email : (optional) » Your comments will be displayed only after manual approval. How many words can be formed from MATHEMATICS if vowels are together?∴ Required number of words = (10080 x 12) = 120960.
How many arrangements are there of the word MATHEMATICS if consonants occur together?Complete step-by-step answer: The word MATHEMATICS consists of 2 M's, 2 A's, 2 T's, 1 H, 1 E, 1 I, 1 C and 1 S. Therefore, a total of 4989600 words can be formed using all the letters of the word MATHEMATICS.
How many vowels does the word MATHEMATICS have?Explanation: In the word MATHEMATICS, the number of consonants are 7 and the number of vowels are 4.
How many ways the word MATHEMATICS can be arranged?This can be done in 8C4 ways as there are 8 different letters(M,T,A,H,E,I,C,S) = 70 ways. Q.
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