How many ways can the letters of the word Missourt be arranged so that the vowels always come together?
In how many different ways can the letters of the word ‘CORPORATION’ be arranged so that the vowels always come together? Show
Answer VerifiedHint: In the given question we are required to find out the number of arrangements of the word ‘CORPORATION’ so that the vowels present in the word always come together. The given question revolves around the concepts of permutations and combinations. We will first stack all the vowels together while arranging the letters of the given word and then arrange the remaining consonants of the word. Complete step-by-step answer: Note: One should know about the principle rule of counting or the multiplication rule. Care should be taken while handling the calculations. Calculations should be verified once so as to be sure of the answer. One must know that the number of ways of arranging n things out of which r things are alike is $ \left( {\dfrac{{n!}}{{r!}}} \right) $ .
How many ways can the letters of the word Missouri be arranged so that all vowels do not occur together answer?Required number of ways = (120 x 6) = 720.
How many ways all vowels come together?The number of ways the word TRAINER can be arranged so that the vowels always come together are 360.
How many ways word arrange can be arranged in which vowels are not together?number of arrangements in which the vowels do not come together =5040−1440=3600 ways.
How many ways the word over expand can be arranged so that all vowels come together?The word EXTRA can be arranged in such a way that the vowels will be together = 4! × 2! The letters of the words EXTRA be arranged so that the vowels are never together = (120 - 48) = 72 ways. ∴ The letters of the words EXTRA be arranged so that the vowels are never together in 72 ways.
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