document.write( "Question 1064532: In how many ways can Ray, Steve, Ben, Ann, Cindy, and Dolly line up so that no two of the three boys are next to each other? \n" ); document.write( "
Algebra.Com's Answer #679875 by Edwin McCravy(20056)![]() ![]() You can put this solution on YOUR website! \r\n" ); document.write( "There are 4 possible line-ups by gender, B=boy, G=girl:\r\n" ); document.write( "\r\n" ); document.write( "BGBGBG\r\n" ); document.write( "GBGBGB\r\n" ); document.write( "BGGBGB\r\n" ); document.write( "BGBGGB\r\n" ); document.write( "\r\n" ); document.write( "For each of those 4 line-ups by gender,\r\n" ); document.write( "\r\n" ); document.write( "The 3 girls can be arranged in 3! or 6 ways\r\n" ); document.write( "The 3 boys can also be arranged in 3! or 6 ways.\r\n" ); document.write( "\r\n" ); document.write( "That's (4)(3!)(3!) = (4)(6)(6) = 144 ways.\r\n" ); document.write( "\r\n" ); document.write( "Edwin\n" ); document.write( " |