document.write( "Question 434741: How many ways can the letters in the word smile be arranged if the first letter must be a vowel? \n" ); document.write( "
Algebra.Com's Answer #301091 by Edwin McCravy(20056)![]() ![]() You can put this solution on YOUR website! How many ways can the letters in the word smile be arranged if the first letter must be a vowel? \n" ); document.write( " \r\n" ); document.write( "There are 2 vowels so there are 2 ways to choose the 1st letter.\r\n" ); document.write( "For each of those 2 ways to choose the 1st letter there are 4 remaining\r\n" ); document.write( " letters to choose for the the 2nd letter. That's 2*4 ways to choose\r\n" ); document.write( " the first 2 letters.\r\n" ); document.write( "For each of those 2*4 ways to choose the 1st 2 letters there are 3 remaining\r\n" ); document.write( " letters to choose for the the 3rd letter. That's 2*4*3 ways to choose\r\n" ); document.write( " the first 3 letters.\r\n" ); document.write( "For each of those 2*4*3 ways to choose the 1st 3 letters there are 2 remaining\r\n" ); document.write( " letters to choose for the the 4th letter. That's 2*4*3*2 ways to choose\r\n" ); document.write( " the first 4 letters.\r\n" ); document.write( "For each of those 2*4*3*2 ways to choose the 1st 4 letters there is only 1\r\n" ); document.write( "remaining letter to choose for the the 5th letter. That's 2*4*3*2*1 ways to\r\n" ); document.write( "choose all 5 letters.\r\n" ); document.write( " \r\n" ); document.write( "So the answer is 2*4*3*2*1 = 48. Here they all are:\r\n" ); document.write( "\r\n" ); document.write( "\r\n" ); document.write( "1. EILMS\r\n" ); document.write( "2. EILSM\r\n" ); document.write( "3. EIMLS\r\n" ); document.write( "4. EIMSL\r\n" ); document.write( "5. EISLM\r\n" ); document.write( "6. EISML\r\n" ); document.write( "7. ELIMS\r\n" ); document.write( "8. ELISM\r\n" ); document.write( "9. ELMIS\r\n" ); document.write( "10. ELMSI\r\n" ); document.write( "11. ELSIM\r\n" ); document.write( "12. ELSMI\r\n" ); document.write( "13. EMILS\r\n" ); document.write( "14. EMISL\r\n" ); document.write( "15. EMLIS\r\n" ); document.write( "16. EMLSI\r\n" ); document.write( "17. EMSIL\r\n" ); document.write( "18. EMSLI\r\n" ); document.write( "19. ESILM\r\n" ); document.write( "20. ESIML\r\n" ); document.write( "21. ESLIM\r\n" ); document.write( "22. ESLMI\r\n" ); document.write( "23. ESMIL\r\n" ); document.write( "24. ESMLI\r\n" ); document.write( "25. IELMS\r\n" ); document.write( "26. IELSM\r\n" ); document.write( "27. IEMLS\r\n" ); document.write( "28. IEMSL\r\n" ); document.write( "29. IESLM\r\n" ); document.write( "30. IESML\r\n" ); document.write( "31. ILEMS\r\n" ); document.write( "32. ILESM\r\n" ); document.write( "33. ILMES\r\n" ); document.write( "34. ILMSE\r\n" ); document.write( "35. ILSEM\r\n" ); document.write( "36. ILSME\r\n" ); document.write( "37. IMELS\r\n" ); document.write( "38. IMESL\r\n" ); document.write( "39. IMLES\r\n" ); document.write( "40. IMLSE\r\n" ); document.write( "41. IMSEL\r\n" ); document.write( "42. IMSLE\r\n" ); document.write( "43. ISELM\r\n" ); document.write( "44. ISEML\r\n" ); document.write( "45. ISLEM\r\n" ); document.write( "46. ISLME\r\n" ); document.write( "47. ISMEL\r\n" ); document.write( "48. ISMLE\r\n" ); document.write( "\r\n" ); document.write( "Edwin\n" ); document.write( " |