What ways the letters of the word cricket can be arranged to form the different new words so that the vowels always come together?
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In how many different ways can the letters of the word TRAINER be arranged so that the vowels always come together?A. 1440B. 120C. 720D. 360Answer Verified
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. OverviewThis tool lists out all the arrangements possible using letters of a word under various conditions. This can be used to verify answers of the questions related to calculation of the number of arrangements using letters of a word. This tool programmatically generates all the arrangements possible. If you want to find out the number of arrangements mathematically, use Permutations Calculator For example, consider the following question. How many words with or without meaning can be formed using the letters of 'CRICKET' such that all the vowels must come together? The answer of the above problem is $720$. Using this tool, it is possible to generate all these $720$ arrangements programmatically. At the same time, Permutations Calculator can be used for a mathematical solution to this problem as provided below. The word 'CRICKET' has $7$ letters where $2$ are vowels (I, E). Vowels must come together. Therefore, group these vowels and consider it as a single letter. Thus we have total $6$ letters where C occurs $2$ times. Number of ways to arrange these $6$ letters All the $2$ vowels are different. Required number of ways Note: This tool uses JavaScript for generating the number of permutations and can be slow for large strings. Add Your Comment(use Q&A for new questions) Name Aptitude Permutation And CombinationPage 2
Answer is: CGiven words contains 8 different letters. When the vowels AUE are always together, we may suppose them to form an entity, treated as one letter.
Answer is: CRequired number of ways = 15C11 = 15C(15 - 11) = 15C4
Answer is: CRequired number of ways = (8C5 x 10C6)
Answer is: CWe may have(1 black and 2 non-black) or (2 black and 1 non-black) or (3 black).
Answer is: BThere are 6 letters in the given word, out of which there are 3 vowels and 3 consonants.
Answer is: ARequired number of ways = 7C5 x 3C2 = 7C2 x 3C1 = [(7 x 6)/(2 x 1) x 3] = 63.
Answer is: CLOGARITHMS contains 10 different letters.
Answer is: CIn the word MATHEMATICS, we treat the vowels AEAI as one letter. CommentsIn what ways the letter of the word actors can arranged so that the vowels occupy only the even position?Q. 3. In what ways the letters of the word ACTORS can arrange so that the vowels occupy only the even positions? ATQ, the vowels A, O can be placed at any of the position out of 2, 4, and 6.
How many ways can the letters of the word Learn be arranged so that the vowels always come together?= 6 ways. Required number of ways = (120 x 6) = 720. In how many different ways can the letters of the word 'CORPORATION' be arranged so that the vowels always come together?
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Exercise :: Permutation and Combination - General Questions.. How many ways a word can be arranged permutation and combination?Required number of ways = (120 x 6) = 720.
How many ways can the letters of the word hacker be rearranged such that the vowels always appear together?Hence the answer would be 3 × 3 × 3 × 3 × 3 × 3 = 36=729 ways.
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