In how many different ways can the letters of the word detail be arranged. Total number of ways = (6 x 6) = 36.

In how many different ways can the letters of the word detail be arranged. For each of those 6 ways to arrange the vowels where the V's are, we can arrange the 3 consonants (D,T,L) to go where the C's are also in 3!=6 ways. Number of ways of arranging the vowels = 3P3 = 3! = 6. Thus, we have MTHMTCS (AEAI). 120 In how many different ways can the letters of the word 'DETAIL' be arranged in such a way that the vowels occupy only the odd positions? View Solution. Since detail has 6 letters, there are 3 odd positions, the 1st, 3rd, and 5th spots. Hence, the total number of words in which vowels occupy odd positions = 3! × 3! = 6 × 6 = 36 ways. 7560 d. There are 3 vowels (E, A, I) and 3 consonants (D, T, L). Number of alike consonants. In how many ways can the letters of the word 'LEADER' be arranged? a. 756. Number of ways of these arrangements = 3 P 3 = 3 ! = 6 . ∴ Required number of ways = (120 x 6) = 720. Let us mark these positions as under: (1) (2) (3) (4) (5) (6) Now, 3 vowels can be placed at any of the three places out 4, marked 1, 3, 5. Was this answer helpful? In how many ways can it be done? a. So arrange them in 7 places and find how the 7 letters can be arranged. Math; Statistics and Probability; Statistics and Probability questions and answers; In how many different ways can the letters of the word “DETAIL” be arranged such that the vowels must occupy only the odd positions? In how many different ways can the letters of the word 'DETAIL' be arranged in such a way that the vowels occupy only the odd positions? View Solution. In how many different ways can the letters of the word ARRANGE be arranged? If the two 'R's do not occur together, then how many arrangements can be made? if besides the two R's the two A's also do not occur together, then how many permutations will be obtained? In how many ways can 8 Indians and, 4 American and 4 Englishmen can be seated in a row so that all person of the same nationality sit together? A. 60: E In how many different ways can the letters of the word 'DETAIL' be arranged in such a way that the vowels occupy only the odd positions? View Solution. In how many different ways can the letters of the word ′ D E T A I L ′ be arranged in such a way that the vowels occupy only the even positions? View Solution Q 4 Click here👆to get an answer to your question ️ In how many different ways can the letters of the word 'DETAIL' be arranged in such a way that the vowels occupy only the even positions? In how many different ways can the letters of the word 'DETAIL' be arranged in such a way that the vowels occupy only the odd positions? A. Number of ways of arranging the vowels = 3 P 3 = 3! = 6. (e) 3 vowels can be arranged in three odd places in 3!ways. 144 c. 32 B. Total letters in word GAMBLE = 6. We can go ahead The word DETAIL has six letters Vowels 3 Thus possible arrangement of vowels 3326 Consonants 3 Thus possiblearrangement of consonants36 Hencethe total number of Dec 22, 2021 · Now, 3 vowels can be placed at any of the three places out 4, marked 1, 3, 5. May 3, 2018 · 1 Answer. Jul 8, 2024 · Similarly, the number of ways to arrange the 3 consonants in 3 positions is: \( P(3, 3) = \frac{3!}{(3-3)!} = \frac{3!}{0!} = 3! = 6 \) Step 5: Calculate the total arrangements To find the total number of arrangements where the vowels occupy the odd positions and the consonants occupy the even positions, we multiply the number of arrangements Apr 4, 2020 · "In how many different ways can the letters of the word ‘DETAIL’ be arranged so that the vowels occupy only the odd positions?" There are 6 letters in the given word, out of which there are 3 vowels and 3 consonants. We can choose the three vowels {E,A,I} to go where the V's are in 3!=6 ways. Mar 6, 2024 · The letters of the word 'detail' can be arranged in (b) (72) different ways such that the vowels occupy only the odd positions. 9! b. Can you explain this answer? for Quant 2024 is part of Quant preparation. Transcribed Image Text: Question 2 In how many different ways can the letters of the word 'DETAIL' be arranged in such a way that the letters A,I, and E occupy only the odd positions? A. Permutation: n Different Things Taken All at a Time When All Are Not Different. Arrange them in even and odd places as there are a total 7 letters in the word. Total number of ways = (6 x 6) = 36. 3! 4! 8! 4! B. Similarly 3 consonants can be arranged in three even places in 3! ways. Let’s determine how many ways the word can be arranged when the vowels occupy the odd positions. You then set up the equation 10! / (2!3!). 3! 8! Jan 22, 2015 · Find an answer to your question In how many different ways can the letters of the word 'DETAIL' be arranged in such a way that the vowels occupy only the odd po… NiamBumb NiamBumb 22. Question How many ways the letters of the word ′ A R M O U R ′ can be arranged? In \[4989600\]distinct ways, the letter of the word ‘Mathematics’ can be written. The repeated letters are "E" (3 times) and "N" (2 times). of ways to arrnage 3 consonant in 4 places = 4 P 3 = 4 × 3 × 2 = 24 ways VIDEO ANSWER: Hello, so here we're looking at the word optical. ∴ Number of ways of arranging letters = 6! = 6 × 5 × 4 × 3 × 2 × 1 = 720. So O -P -T -I -C -A -L. 5880 c. The word 'OPTICAL' contains 7 different letters. 72 b. In how many different ways can the letters of the word ′ D E T A I L ′ be arranged in such a way that the vowels occupy only the even positions? View Solution Feb 21, 2021 · How many letters are in the word attractive? There are 10 letters. Number of ways in which n letter can be arranged = n! Calculation. 48: C. Number of letter A = 2 In how many ways can 8 Indians and, 4 American and 4 Englishmen can be seated in a row so that all person of the same nationality sit together? A. The total number of ways to arrange the letters in the word 'DETAIL' is 6!/ (2!)=360. Number of letters = 8 . They can occupy 1st, 3rd and 5th position in any order. Number of "DIFFERENT" be arranged?The word "DIFFERENT" has a total of 9 letters. Wanna know how many ways the letters can be arranged such that the vowels are going to be together. Explanation. 12. Apr 16, 2024 · Ex 6. ∴ Required number of ways = (2520 x 20) = 50400. Number of vowels = 4. SOLUTION. The number of ways in which the letters of the word ′ A R R A N G E ′ can be arranged so that the two R 's are never together is. Let the positions be marked as (1)(2)(3)(4)(5)(6) Click here:point_up_2:to get an answer to your question :writing_hand:in how many ways can the letters of the word apple be arranged Click here:point_up_2:to get an answer to your question :writing_hand:in how many different ways can the letters of the word detail be arranged in 2 In how many different ways can the letters of the word 'DETAIL' be arranged in such a way that the vowels occupy only the odd positions? a) 32 b) 48 c) 36 d) 60 e) 120 In how many different ways can the letters of the word 'DETAIL' be arranged in such a way that the vowels occupy only the odd positions? A. There are 6 letters in the word DETAIL. 120 Expert Solution In how many different ways can the letters of the word DETAIL be arranged such that the vowels must occupy only the odd positions?a)36b)64c)120d)None of theseCorrect answer is option 'A'. 564 b. Concept. Word permutations calculator to calculate how many ways are there to order the letters in a given word. The number of times letter E is present = 2. In how many different ways can the letters of the word THOUGHTS be arranged so that the vowels always come together? Solution: Given word: THOUGHTS . 48. factorial The product of an integer and all the integers below it letter arrangements in a word permutation a way in which a set or number of things can be ordered or arranged. Verified. 3, 11 In how many ways can the letters of the word PERMUTATIONS be arranged if the words start with P and end with S Let first position be P & last position be S (both are fixed) Since letters are repeating Hence we use this formula 𝑛!/𝑝1!𝑝2!𝑝3! Total number of letters = n = Mar 28, 2019 · In how many different ways can the letters of the word DETAIL be arranged in such a way that the vowels occupy only the odd positions? asked May 3, 2018 in Aptitude by shabnam praween ( 138k points) Click here:point_up_2:to get an answer to your question :writing_hand:in how many ways the letters of the word leader can be arranged In how many different ways can the letters of the word BANKING be arranged in such a way that the vowels always come together? a) 120 b) 240 c) 360 d) 540 e) 720 Jul 15, 2024 · Given. So, the number of letters for arrangement = 7 . Step 1/9 1. Well, the vowels here are gonna be O -I -N -A. 120. i. Find the number of permutations of the letters of the word ALLAHABAD. (46 ways), How many 4 digit numbers that are divisible by 10 can be formed from the numbers 3, 5, 7, 8, 9, 0 such that no number repeats? (60), Find the number of permutations of the letters of In how many ways, the letters of the word 'STRESS' can be arranged? Sep 7, 2022 · The number of ways in which the word detail can be arranged in such a way that the vowels occupy only the odd positions is 36. Now we have 3 consonants and 4 places. There are 6 letters in the given word, out of which there are 3 vowels and 3 consonants. 32: B. Also, the 3 consonants can be arranged at the remaining 3 positions. Number of alike vowels. 2015 In how many different ways can the letters of the word 'DESIGN' be arranged so that the vowels are at the two ends? Click here:point_up_2:to get an answer to your question :writing_hand:in how many different ways can the letter of the word total be arranged e 3 vowels can be arranged in three odd places in 3!ways. How many letters are repeated? A is repeated 2 times and t is repeated 3 times. Calculation: The number of letter in LEADER = 6. , (OU)THGHTS . Now, 5 letters can be arranged in 5! = 120 ways. In how many different ways can the letters of the word DETAIL be arranged in such a way that the vowels occupy only the odd positions? (a) 120 (b) 60 (c) 48 (d) 32 In how many different ways can the letters of the word 'DETAIL' be arranged in such a way that the vowels occupy only the odd positions? Q. Then, we have to arrange the letters PTCL (OIA). Since there are repeated letters in the word, we need to consider the number of ways to arrange the letters taking into account the repeated letters. When the vowels (E, A, I) are in odd positions, there are 3! ways to arrange them in the odd positions and 3! ways to arrange the remaining consonants in the even positions. Sep 23, 2022 · Answer. The vowels must occupy odd positions, which means they can only be in positions 1, 3, and 5. When the vowels OIA are always together, they can be supposed to form one letter. In how many ways can the letters of the word B I L A S P U R be arranged so that three vowels may never be put together? Q. If each of the vowels in the word 'MEAT' is kept unchanged and each of the consonants is replaced by the previous letter in the English alphabet, how many four-lettered meaningful words can be formed with the new letters, using each letter only once in each word? Also, the 3 consonants can be arranged at the remaining 3 positions. Q2. Study with Quizlet and memorize flashcards containing terms like Among a set of 5 black balls and 3 red balls, how many selections of 5 balls can be made such that at least 3 of them are black balls. To solve the problem of arranging the letters of the word "DETAIL" such that the vowels occupy only the odd positions, we can follow these steps: Step 1: Identify the letters and their types The word "DETAIL" consists of 6 letters: - Vowels: E, A, I (3 vowels) - Consonants: D, T, L (3 consonants) Step 2: Determine the positions available for In how many different ways can the letters of the word 'DETAIL' be arranged in such a way that the vowels occupy only the odd positions? 32. In the word FAILURE, there are 4 odd position for letters and 3 even positions. 5! 13. 360 d. In how many different ways can the letters of the word 'DETAIL' be arranged in such a way that the vowels occupy only the odd positions? View Solution. H’s = 2 . 36: D. Using all the letters of the word ARRANGEMENT how many different words using all letters at a time can be made such that both A, both E, both R both N occur together . 01. Thus, the number of ways to arrange the letters of the word "DIFFERENT" can be calculated using the formula for Also, the 3 consonants can be arranged at the remaining 3 positions. Explanation: To find the number of arrangements where the vowels (e, a, i) occupy only the odd positions, we first determine the number of odd positions available. 645 c. In how many ways can the letters of the word vowels be arranged, if the letters o e can only occupy odd places. Let the positions be marked as (1)(2)(3)(4)(5)(6) The 3 vowels can be placed at any of the 3 places marked (1)(3)(5) 2. Number of ways of arranging the vowels = 3P 3 =3! = 6. Number of vowels = 2 (O, U) Vowels should come together. Number of ways of these arrangements = 3P3 = 3! = 6. Similarly, 3 consonants can be arranged in three even places in 3! ways. 3! 8! Now, 5 vowels in which O occurs 3 times and the rest are different, can be arranged in 5! 3! = 20 ways. Q5. In this calculation, the statistics and probability function permutation (nPr) is employed to find how many different ways can the letters of the given word be arranged. Let us mark these positions as under: (1) (2) (3) (4) (5) (6) Now, 3 vowels can be placed at any of the three places, marked 1, 3, 5. (i) When vowels are taken together: In the word ‘Mathematics’, we treat the vowels A, E, A, I as one letter. The total number of ways = 6!/2! CSC Numerical Ability Question Solution - In how many different ways can the letters of the word 'DETAIL' be arranged in such a way that the vowels occupy only the odd positions? A. T’s = 2 . Number of letter M = 2 Number of letter T = 2 . Now, we have to arrange letters, out of which M occurs twice, T occurs twice, and the rest are different. The vowels are E, A and I. Word = GAMBLE. a. Step 2/9 2. No. Hint: Find the number of vowels and consonants in the word ‘ARTICLE’. 3! x 3! 3! + 4! 3! x 4! 6! / 3! The total number of arrangements which can be made out of the letters of the word " A l g e b r a " without altering the relative positions of vowels and consonants is Medium View solution Number of consonants = 7. 36. Step 3/9 3. 60. 735 d. 60 E. 48 C. The vowels (OIA) can be arranged among themselves in 3! = 6 ways. e. We will find the number of permutations in which the word DETAIL can be arranged such that the vowels occupy odd positions. 36 D. 11. Given: The word is 'LEADER'. 720. Hence the total number of words in which vowels occupy odd positions = 3! × 3! = 6 × 6 = 36 ways. This is the total # of letters factorial divided by the # of times a letter is repeated factorial. The correct option is C 36. ahq fxxbqx ajfa jsb hvncn fujmg euo qznd sgilcx tubcpx