How many different ways can the letters of the word maruthi be arranged so the vowels are placed 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). 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 ways can letter be arranged so that the vowels always come together?The number of ways the word TRAINER can be arranged so that the vowels always come together are 360.
How many ways can vowels be arranged?The vowels (EAI) can be arranged among themselves in 3! = 6 ways. Required number of ways = (120 x 6) = 720.
How many different ways can letters be arranged?=360 the number of 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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