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Calculation: The word PROBABILITY has 11 letters out of which 4 (O, A, I, I) are vowels and 7 (P, R, B, B, L, T, Y) are consonants. Since no two vowels can be together, we will first arrange the remaining 7 consonants. The consonant can be arranged in \(\rm \dfrac{7!}{2!}=2520\) ways. Now, the 4 vowels can be arranged in any of the 8 spaces between the consonants, as illustrated by a _ below: _ P _ R _ B _ B _ L _ T _ Y _. Number of ways of selecting some 4 places out of the 8 places = \(\rm ^8C_4 = \dfrac{8!}{4!(8 - 4)!}=70\). Number of ways in which the 4 vowels can be arranged in these 4 places = \(\rm \dfrac{4!}{2!}=12\) ∴ The total number of possible arrangements = 2520 × 70 × 12 = 21,16,800.
Sponsored LinksChallenger of the Day Dr.Dipin Singh India Gujarat Time: 00:04:06 Maths Quotes"The gaming of numbers is called maths.So participate in this wonderful game and explore in it,learn in it and enjoy in it.Then only you can pass in this wonderful game." Kumar Purnendu mathematics never dies because it always stays in the minds and souls of people who love mathematics. Those people will not let maths die instead they will die................. D . kalyan kumar Placed User CommentsM4Math helped me a lot. Vipul Chavan 2 years ago Thanks m4 maths for helping to get placed in several companies. yash mittal 2 years ago 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 C14400The explanation for the correct answer.Find the number of ways such that no two vowels occur together.Given: TRIANGLEThe 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!= 302403.The number of ways where all vowels occur together =C3×6!×3!= 43203.Therefore required number of words =40320-30240+4320=14400.Hence option (C) is the correct answer.Get the answer to your homework problem. Try Numerade free for 7 days Christopher G. Algebra 6 months ago We don’t have your requested question, but here is a suggested video that might help. In how many ways can the letters of the word number be arranged? FRACTION vowels = AIO, let k FRCTNK 6! => 6X5X4X3X2X1= 720 so, 720 ways can be arranged without two vowels are together. total ways in which the letters of the word FRACTION can be arranged = 8! = 40320 vowels : A I O ( let us consider them as 1 letter instead of 3 letters and let this new letter be * ) consonants : F R C T N now the new word thus formed will be : * F R C T N the letters of this new word can be arranged in 6! ways. not only that * can arrange itself in 3! ways so the total ways in which all the vowels are together = 6! x 3! = 4320 so total words that can be formed so that no two vowels are together = 40320 - 4320 = 36000 Here is the answers MATHEMATICS IS LIKE TRUE LOVE- A SIMPLE IDEA BUT CAN GET COMPLICATED... Ricky GakharMathematics is a Zeal.. If u are spending your time with Mathematics, I am sure you will never care about your watch..! Ravi Ranjan OjhaHow many ways the letters of word fraction be arranged so that no two vowels are together?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.
How many different ways can the letters of the word combine be arranged so that the vowels always come together?The number of ways the word TRAINER can be arranged so that the vowels always come together are 360.
How many ways can Fractions be arranged?There are two common methods of ordering fractions.
These are: Using a common denominator. Changing fraction to decimals and then ordering.
What is the fraction of vowels in the word fraction?Expert-verified answer
There are 5 vowels, which are a,e,i,o,u. In word mathematics, their are 4 vowels which are a,e,a,i. and the total no. of letters in mathematics are 11. The fraction of the letters are vowels will be
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