How many words are there in which vowels are never together?
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1.Find the no. of permutations of letters a , b , c , d, e , f , g taken all at a time if neither “beg” nor “cad” patterns appear in any word. 2.Find the no. of ways in which letter sof the word SQUARE can be arranged such that: A) Vowels are always together. B)vowels are never together. C)No. of ways in which none of U , A , E are together. I find such question super confusing….as they involve a few extra steps I guess….i’m grateful if you can take out the time to answer any of these if you know them. You tips and help would is highly appreciated . Thank you! #2 2. SQUARE a) Vowels are always together Note that the vowels can appear in any one of these positions [ V = vowel ] V V V _ _ _ _ V V V _ _ _ _ V V V _ _ _ _ V V V There are 4 positions where the vowels can appear together.....and for each of these the vowels can be arranged in 3! ways = 6 ways and the other letters can be arranged in 3! = 6 ways So......the total possible "words" that can be made where the vowels appear together is 4 * 6 * 6 = 144 "words" = 144 arangements b) Vowels are never together The vowels can appear in these positions V _ V _ V _ _ V _ V _ V So there are 2 possibilities here.....and for each of these, the vowels can be arranged in 3! ways = 6 ways and the other 3 letters can be arranged in 3! ways = 6 ways So.....the total possible arrangements where the vowels never appear together is just : 2 * 6 * 6 = 72 arrangements c) UAE never appear together First note that the total possible arrangements is just 6! = 720 Let's count the number of arrangements whereUAE do appear together U A E _ _ _ _ U A E _ _ _ _ U A E _ _ _ _ U A E There are 4 of these....and for each, the other letters can be arranged in 3! = 6 ways So....the total arrangements where UAE appear together is just : 4 * 3! = 4 * 6 = 24 So....the number of arrangements where UAE never appear together is just Total arrangements - Arrangements where UAE appear together 720 - 24 = 696 arrangements #7 CPhill i think theres some problem in the 'c' parts answer becoz my teachers answer is 144. its somewhat like: No. of ways in which none of U , A , E are together = 3! x 4P3 = 3! x 4!/1! = 3! x 4! = 144. i have no idea what is done here. dont you think that U, A , E ..that are vowels...and when they wont appear together, then the answer will be the same as the 'b' part???? #8 C) The 3 letters "UAE" appear in 6 - 3 + 1 = 4 positions. IF these letters are allowed to permute, that is: UAE, UEA, AEU......etc. Then, you will have: 4 positions x 3! =24 permutations. The remaining 3 letters, S, R, Q will permute in 3! ways =6 ways. So the total permutations will be: 4 x 3! x 3! =4 x 6 x 6 = 144 permutations. #9 1.Find the no. of permutations of letters a , b , c , d, e , f , g taken all at a time if neither “beg” nor “cad” patterns appear in any word. Mmm I'd put a rope around beg then that makes a,c,d,f (beg) so there will be 5!= 120 permutations If I put a rope around (cad) that will also be 120 permutaions BUT some of these permutations are in both so if I put a rope around (cad) and (beg) that will be 3! =6 permutations. so altogether the number of permutaions that include the words beg or cad is 120+120-6= 234 permutations. Without any restrictions there are 7! = 5040 permutations so the number of permutation without beg or cad is 5040 - 234 = 4806 2.Find the no. of ways in which letters of the word SQUARE can be arranged such that: A) Vowels are always together. SQR (UAE) UAE can be arranged in 3!=6 ways and SQR(UAE) can be arranged in 4!=24 ways. So altogether that is 24*6 = 144 ways B)vowels are never together. There are 3 vowels and 3 consonants so the choices are CVCVCV or VCVCVC 3!*3!*2 = 6*6*2 = 72 ways C)No. of ways in which none of U , A , E are together. (in any order) Again, UAE must be in the 1st 3rd and 5th positions or in the 2nd 4th and 6th positions. I do not think there are any other choices so it is the same as the question above I think. Maybe I have misunderstood the question? 72 ways What do you think Rosala, do you question any of my answers (which is perfectly fine) or do you have any questions for me? 7 Online UsersHow many words can be formed so that vowels are never together?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 words are there in Rainbow in which vowels are never together?This result 4320 is overcounting since it is only considering the fact that all vowels come together only and not the case where only two vowels can also come together also, as the question says vowels are never together, and not that all the vowels are not together only. This is why the correct answer is 1440.
Do all the vowels never occur together?1 Answer. Condition: vowels should never occur together. There are 6 letters in the word GOLDEN in which there are 2 vowels. Total number of words – total number of words in which the vowels come together.
How many vowels are there in Rainbow?RAINBOW has 4 Consonants and 3 vowels.
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