How many ways can letter of the word fraction be arranged so that two vowels are together?
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No worries! We‘ve got your back. Try BYJU‘S free classes today! No worries! We‘ve got your back. Try BYJU‘S free classes today! Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses No worries! We‘ve got your back. Try BYJU‘S free classes today! Solution The correct option is C14400 The explanation for the correct answer.Find the number of ways such that no two vowels occur together.Given: TRIANGLE (adsbygoogle = window.adsbygoogle || []).push({}); The total number of letters in the word triangle is 8.The total number of words that can be formed =8!=40320.The total number of words in which two vowels occur together =C2×7!×2!=30240 3.The number of ways where all vowels occur together =C3×6!×3!=4320 3.Therefore required number of words =40320-30240+4320=14400.Hence option (C) is the correct answer.The number of ways in which the letters of the word TRIANGLE can be arranged such that two vowels not occur together is (a) 1200(b) 2400(c) 14400(d) none of theseAnswer Verified
Hint: In this question, we first need to find the total number of arrangements possible with the given letters of the word using the permutation formula given by \[{}^{n}{{P}_{r}}\]. Then we need to find the number of words in which two vowels are together but first selecting the two vowels and then arranging all the letters using the formula \[{}^{n}{{C}_{r}}\]. Now, find the number of words in which 3 vowels are together and then subtract 2 vowels together from total words and add 3
vowels together.Complete step by step solution: Note: total ways in which the letters of the word FRACTION can be arranged = 8! = 40320 How many ways the letters of word fraction be arranged so that no two vowels are together?Step-by-step explanation:
Fraction consists of 8 letters which has 3 vowels (a, I, o) and rest 5 are consonants. It can be -F- R- C- T- N so that no 2 vowels are together. Now 3 vowels can fill these 6 places in (6,3) ways.
What fraction of letters are vowels?Two of those letters, or 2/6 of the letters, are vowels, and four of the letters, or 4/6, are consonants.
How many ways Word arrange can be arranged in which vowels are together?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 n! r!
How many ways can you arrange the vowels?The vowels (EAI) can be arranged among themselves in 3! = 6 ways. Required number of ways = (120 x 6) = 720.
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