document.write( "Question 1143486: In how many different ways can the letters of \"SUNDAY\" be arranged?
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document.write( "How many of these arrangements begin with an \"S\"?
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document.write( "How many begin with \"S\" but do not end with a vowel? \n" );
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Algebra.Com's Answer #764322 by Edwin McCravy(20056)![]() ![]() You can put this solution on YOUR website! In how many different ways can the letters of \"SUNDAY\" be arranged? \n" ); document.write( " \r\n" ); document.write( "6 choices for the 1st letter, \"S,U,N,D,A,Y\" for which there are\r\n" ); document.write( "5 choices for the 2nd letter, for which there are\r\n" ); document.write( "4 choices for the 3rd letter, for which there are\r\n" ); document.write( "3 choices for the 4th letter, for which there are\r\n" ); document.write( "2 choices for the 5th letter, for which there are\r\n" ); document.write( "1 choice for the 6th letter.\r\n" ); document.write( "\r\n" ); document.write( "That's 6∙5∙4∙3∙2∙1 = 6! = 720 ways\r\n" ); document.write( " \n" ); document.write( "How many of these arrangements being with \"S\"? \n" ); document.write( " \r\n" ); document.write( "1 choice for the 1st letter, \"S\", for which there are\r\n" ); document.write( "5 choices for the 2nd letter, \"U,N,D,A,Y\", for which there are\r\n" ); document.write( "4 choices for the 3rd letter, for which there are\r\n" ); document.write( "3 choices for the 4th letter, for which there are\r\n" ); document.write( "2 choices for the 5th letter, for which there are\r\n" ); document.write( "1 choice for the 6th letter.\r\n" ); document.write( "\r\n" ); document.write( "That's 1∙5∙4∙3∙2∙1 = 1∙5! = 120 ways\r\n" ); document.write( " \n" ); document.write( "How many begin with \"S\" but do not end with vowel? \n" ); document.write( " \r\n" ); document.write( "1 choice for the 1st letter, \"S\", for which there are\r\n" ); document.write( "2 choices for the 6th letter, \"U,A\", for which there are\r\n" ); document.write( "4 choices for the 2nd letter, for which there are\r\n" ); document.write( "3 choices for the 3rd letter, for which there are\r\n" ); document.write( "2 choices for the 4th letter, for which there are\r\n" ); document.write( "1 choice for the 5th letter.\r\n" ); document.write( "\r\n" ); document.write( "That's 1∙2∙4∙3∙2∙1 = 2∙4! = 4∙24 = 96 ways\r\n" ); document.write( "\r\n" ); document.write( "Edwin\n" ); document.write( " |