Recommended textbooks for you College Algebra (MindTap Course List) Author:R. David Gustafson, Jeff Hughes Publisher:Cengage Learning College Algebra Publisher:Cengage Learning Holt Mcdougal Larson Pre-algebra: Student Edition... Algebra & Trigonometry with Analytic Geometry Algebra and Trigonometry (MindTap Course List) Author:James Stewart, Lothar Redlin, Saleem Watson Publisher:Cengage Learning College Algebra (MindTap Course List) ISBN:9781305652231 Author:R. David Gustafson, Jeff Hughes Publisher:Cengage Learning College Algebra ISBN:9781337282291 Author:Ron Larson Publisher:Cengage Learning Holt Mcdougal Larson Pre-algebra: Student Edition... ISBN:9780547587776 Author:HOLT MCDOUGAL Publisher:HOLT MCDOUGAL Algebra & Trigonometry with Analytic Geometry ISBN:9781133382119 Author:Swokowski Publisher:Cengage Algebra and Trigonometry (MindTap Course List) ISBN:9781305071742 Author:James Stewart, Lothar Redlin, Saleem Watson Publisher:Cengage Learning How many ways can the letters of the word FRIEND be arranged so that the vowels come together? In a school sinaina competition with contestants $\begingroup$
In the below solved problem, every thing is okay, but if we have $4$ consonants then why we are giving $5!$? and is this a combination problem? how to distinguish? Question: In how many different ways can the letters of the word 'OPTICAL' be arranged so that the vowels always come together? Answer: The word 'OPTICAL' contains $7$ different letters. When the vowels OIA are always together, they can be supposed to form one letter. Then, we have to arrange the letters PTCL (OIA). Now, $5$ letters can be arranged in $5! = 120$ ways. The vowels (OIA) can be arranged among themselves in $3! = 6$ ways. Required number of ways $= (120*6) = 720$. $\endgroup$ |