How many ways can be letter of the word MATHEMATICS be arranged so that the vowels always come together?
Show
Text Solution `(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. Discussion :: Permutation and Combination - General Questions (Q.No.13)
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 ways can the letters in MATHEMATICS be arranged?There are 24 different ways to arrage the letters in the word math .
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?
|