How many ways can the letters of the word MATHEMATICS be arranged so that the vowels always come together?
In how many different ways the letters of the word “MATHEMATICS” can be arranged so that the vowels always come together ? Show
A. 10080 B. 4989600 C. 120960 D. None of these In the word ‘MATHEMATICS’, we treat the vowels AEAI as one letter. Thus, we have MTHMTCS (AEAI). `(8!xx4!)/(2!2!)``(8!xx4!)/(2!2!2!)``(8!)/(2!2!2!)``(8!)/(4!2!2!)` Answer : B Solution : There are 4 vowels viz. A,E, A, I. Considering these four vowels as one letter we have 8 letteres (M, T, H, M, T, C, S and one letter obtained by combining all vowels), out of which M occurs twice, T occurs twice and the rest all different. In how many words can the letters of word ‘Mathematics’ be arranged so that (i) vowels are together (ii) vowels are not togetherAnswer Verified
Hint: First find the number of ways in which word ‘Mathematics’ can be written, and then we use permutation formula with repetition which is given as under, Complete step by step solution: (i) When vowels are taken together: (ii) When vowels are not taken together: Note: In this type of question, we use the permutation formula for a word in which the letters are repeated. Otherwise, simply solve the question by counting the number of letters of the word it has and in case of the counting of vowels, we will consider the vowels as a single unit.
How many ways can the letters in MATHEMATICS be arranged?There are 24 different ways to arrage the letters in the word math .
How many ways can the letters of the word MATHEMATICS be arranged so that the vowels always come?Now, we have to arrange 8 letters, out of which M occurs twice, T occurs twice and the rest are different. ∴ Number of ways of arranging these letters =8!/(2!)( 2!) = 10080.
How many words can be made from the word MATHEMATICS in which vowels are together?Total no of cases in which the word MATHEMATICS can be written = 11! = 8! Hence, the number of words can be made by using all letters of the word MATHEMATICS in which all vowels are never together is 378000.
How many ways to arrange the letters in MATHEMATICS if the vowels are always together at the end of word?120960 ways . Originally Answered: In how many different ways can the letters of the word mathematics be arranged so that the vowels always come together?
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