document.write( "Question 270350: An urn contains 4 red, 2 white, and 2 blue marbles. In how many ways can three marbles be selected so that at least one of them is blue? \n" ); document.write( "
Algebra.Com's Answer #198091 by Edwin McCravy(20055)\"\" \"About 
You can put this solution on YOUR website!
An urn contains 4 red, 2 white, and 2 blue marbles. In how many ways can three marbles be selected so that at least one of them is blue?
\n" ); document.write( "
\r\n" );
document.write( "There are two methods:\r\n" );
document.write( "\r\n" );
document.write( "First method:\r\n" );
document.write( "\r\n" );
document.write( "We add the number of ways defined by these cases:\r\n" );
document.write( "\r\n" );
document.write( "Case 1:  We pick both blue balls and one non-blue ball\r\n" );
document.write( "\r\n" );
document.write( "Case 2:  We pick 1 blue ball and 2 non-blue balls\r\n" );
document.write( "\r\n" );
document.write( "For case 1, we pick both blue balls 1 way, then the other ball,\r\n" );
document.write( "any of 6 ways.  That's 1x6 = 6 ways\r\n" );
document.write( "\r\n" );
document.write( "For case 2, we pick the blue ball either of 2 ways, then the \r\n" );
document.write( "2 non-blue ball, any of 6C2 ways.  That's 2x15 = 30 ways.\r\n" );
document.write( "\r\n" );
document.write( "So the total number of wasy is 6 + 30 = 36\r\n" );
document.write( "\r\n" );
document.write( "--------------------------------\r\n" );
document.write( "\r\n" );
document.write( "Second method:\r\n" );
document.write( "\r\n" );
document.write( "The number of ways of picking ANY 3 balls from the 8 balls\r\n" );
document.write( "\r\n" );
document.write( "             MINUS\r\n" );
document.write( "\r\n" );
document.write( "the number of ways of picking 3 NON-blue balls from the 6 NON-blue balls.\r\n" );
document.write( "\r\n" );
document.write( "That's 8C3 - 6C3 =  56 - 20 = 36 ways.\r\n" );
document.write( "\r\n" );
document.write( "Either way gives the same answer.\r\n" );
document.write( "\r\n" );
document.write( "Edwin
\n" ); document.write( "
\n" );