In how many ways the word grapes can be arranged so that vowels are always together
Free Show Electric charges and coulomb's law (Basic) 10 Questions 10 Marks 10 Mins The formula to find a number of ways word can be arranged, so that the vowels do not come together is: Total word(factorial) - (Total word - 1)factorial × (number of vowels)factorial Given: Total words = 5 Total word - 1 = 4 Number of vowels = 2 Substituting in the formula: 5! - (4! × 2!) = 120 - 48 = 72 Hence, 72 ways are there to arrange SCALE so that vowels do not come together. Latest Airforce Group X Updates Last updated on Nov 11, 2022 IAF Group X Provisional Select List List released for 01/2022 intake. The Indian Air Force (IAF) has also released the official notification for the IAF Group X (01/2023) on 7th November 2022. The selection of the candidates will depend on three stages which are Phase 1 (Online Written Test), Phase 2 ( DV, Physical Fitness Test, Adaptability Test I & II), and Phase 3 (Medical Examination). The exam is scheduled from 18th to 24th January 2023. The candidates who will qualify all the stages of selection process will be selected for the Air Force Group X posts & will receive a salary ranging of Rs. 30,000. This is one of the most sought jobs. Candidates can check the Airforce Group X Eligibility here. Ace your Mathematics and Permutations and Combinations preparations for Word Problems with us and master Mixed Permutation and Combination problems for your exams. Learn today!
Correct Answer:
Description for Correct answer: Therefore, Number of arrangements = \( \Large 5! \times 2! \) = \( \Large 5 \times 4 \times 3 \times 2 \times 1 \times 1 \times 2 \) = 240 Part of solved Permutation and combination questions and answers : >> Aptitude >> Permutation and combination Answer 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. How many ways the word grapes can be arranged?= 5*4*3*2*1 = 120 ways.
How many ways combine can be arranged so that vowels always together?The number of ways the word TRAINER can be arranged so that the vowels always come together are 360.
How many arrangements vowels occur together?Also, O and E may be arranged among themselves in 2! ways . Number of arrangements with vowels together `=(120 xx 2)=240. ` Number of arrangements with vowels never together `=(720-240)=480. How many ways word arrange can be arranged in which vowels are not together?Hence, the answer is 36.
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