How many ways word arrange can be arranged in which vowels are not together?
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. Show
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
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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 to arrange a word orange in which vowels are not together?Answer. So in total there are 6*6*4=144 different ways to arrange the letters of ORANGE so that none of the vowels are next to eachother.
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.
How many ways can we arrange the word parallel that the vowels are kept together?Solution : The given word 'PARALLEL' has 8 letters, out of which there are 2 A's, 3 L's, 1 P, 1 R and 1 E.
Number of their arrangements `=(8!)/((2!) xx(3!)) =3360. 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.
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