In how many ways the word over expand can be arranged so that all vowels come together
Answer Show
Hint: To solve this problem we have to know about the concept of permutations and combinations. But here a simple concept is used. In any given word, the number of ways we can arrange the word by jumbling the letters is the number of letters present in the word factorial. Here factorial of any number is the product of that number and all the numbers less than that number till 1. Complete step by step answer: The number of ways the word TRAINER can be arranged so that the vowels always come together are 360. Note: Here while solving such kind of problems if there is any word of $n$ letters and a letter is repeating for $r$ times in it, then it can be arranged in $\dfrac{{n!}}{{r!}}$ number of ways. If there are many letters repeating for a distinct number of times, such as a word of $n$ letters and ${r_1}$ repeated items, ${r_2}$ repeated items,…….${r_k}$ repeated items, then it is arranged in $\dfrac{{n!}}{{{r_1}!{r_2}!......{r_k}!}}$ number of ways. 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. Nội dung chính Show
Nội dung chính Show
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:
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 letter MATHEMATICS be arranged so that the vowels always come together?∴ Required number of words = (10080 x 12) = 120960. 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. How many arrangements can be made by the letters of the word MATHEMATICS in how many of them vowels are i Together II not together?The word MATHEMATICS consists of 2 M's, 2 A's, 2 T's, 1 H, 1 E, 1 I, 1 C and 1 S. Therefore, a total of 4989600 words can be formed using all the letters of the word MATHEMATICS. 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 so that vowels come together?The number of ways the word TRAINER can be arranged so that the vowels always come together are 360. Note: Here while solving such kind of problems if there is any word of n letters and a letter is repeating for r times in it, then it can be arranged in n! r! How many ways word arrange can be arranged in which vowels are together?Hence, the answer is 36. How many ways leading can be arranged so that vowels come together?∴∴ Required number of ways = (120 x 6) = 720. How many ways can you arrange the vowels?The vowels (EAI) can be arranged among themselves in 3! = 6 ways. Required number of ways = (120 x 6) = 720. How many ways Word arrange can be arranged in which vowels are together?The number of ways the word TRAINER can be arranged so that the vowels always come together are 360. Note: Here while solving such kind of problems if there is any word of n letters and a letter is repeating for r times in it, then it can be arranged in n!
How many ways the word impossible can be arranged so that all the vowels come together?In how many ways can the letters of the word IMPOSSIBLE be arranged so that all the vowels come together? Now count the ways the vowels in the super letter can be arranged, since there are 4 and 1 2-letter(I'i) repeat the super letter of vowels would be arranged in 12 ways i.e., (4!/2!) = (7!/2! × 4!/2!)
How many ways can the letters be arranged so that all the vowels come together word is corporation?So, the total number of ways of arranging the letters of the word 'CORPORATION' be arranged so that the vowels always come together are 7!
How many ways the word apple can be arranged so that vowels always come together?Thus, the number of ways in which apple can be arranged such that vowels come together is equal to 48 ways.
|