How many ways the word mobile can be arranged so that vowels always come together?
Correct option (B) 36 Show
The word ‘MOBILE’ has three even places and three odd places. It has 3 consonants and 3 vowels. In three odd places we have to fix up 3 consonants, which can be done in 3P3 ways. Now in the remaining three places we have to fix up the remaining three vowels, which can be done in 3P3 ways. Therefore, the total number of ways = 3P3 x 3P3 = 36. Answer Verified Hint: 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) $ . Permutation is known as the process of organizing the group, body, or numbers in order, selecting the body or numbers from the set, is known as combinations in such a way that the order of the number does not matter. In mathematics, permutation is also known as the process of organizing a group in which all the members of a group are arranged into some sequence or order. The process of permuting is known as the repositioning of its components if the group is already arranged. Permutations take place, in almost every area of mathematics. They mostly appear when different commands on certain limited sets are considered. Permutation Formula In permutation r things are picked from a group of n things without any replacement. In this order of picking matter.
Combination A combination is a function of selecting the number from a set, such that (not like permutation) the order of choice doesn’t matter. In smaller cases, it is conceivable to count the number of combinations. The combination is known as the merging of n things taken k at a time without repetition. In combination, the order doesn’t matter you can select the items in any order. To those combinations in which re-occurrence is allowed, the terms k-selection or k-combination with replication are frequently used. Combination Formula In combination r things are picked from a set of n things and where the order of picking does not matter.
In how many ways can the letters of the word IMPOSSIBLE be arranged so that all the vowels come together?Solution:
Similar Questions Question 1: In how many ways can the letters be arranged so that all the vowels came together word is CORPORATION? Solution:
Question 2: In how many different ways can the letters of the word ‘MATHEMATICS’ be arranged such that the vowels must always come together? Solution:
Question 3: In How many ways the letters of the word RAINBOW be arranged in which vowels are never together? Solution:
How many different words can be formed with the letters of the word mobile?The number of words which can be made out of the letters of the word MOBILE' when consonants always occupy odd places is \( f \) \( F \) \( F \) \( F \) 72. Was this answer helpful?
How many different ways computer can be arranged so that vowels always come together?Therefore, there are 56 ways to arrange COMPUTER, given the above constraint. Alternatively we can choose to position the vowels first. We will get C(8,3) = 56 ways to select a combination of positions on which the vowels must stay.
How many ways the word apple can be arranged so that vowels always come together?Answer: 60 different ways.
How many ways the word vowel can be arranged so that the vowels come together?So by adding up three we get 48+48+48=144 is the required solution.
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