document.write( "Question 1162129: A box contains 4 red, 4 white and 5 green balls.Three balls are drawn from the
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document.write( "box together. Find the probability that they may be
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document.write( "i) all the same color
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document.write( "ii) all different colors? \n" );
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Algebra.Com's Answer #785844 by Edwin McCravy(20056)![]() ![]() You can put this solution on YOUR website! Find the probability that they may be \n" ); document.write( "i) all of same color. \n" ); document.write( " \r\n" ); document.write( "There are 4+4+5=13 balls. So the number of ways to draw any 3 of them is\r\n" ); document.write( "13C3 = (13∙12∙11)/(3∙2∙1) = 286 ways.\r\n" ); document.write( "\r\n" ); document.write( "The number of ways they can be all red is 4C3 = (4∙3∙2)/(3∙2∙1) = 4 ways.\r\n" ); document.write( "\r\n" ); document.write( "The number of ways they can be all white is 4C3 = (4∙3∙2)/(3∙2∙1) = 4 ways.\r\n" ); document.write( "\r\n" ); document.write( "The number of ways they can be all green is 5C3 = (5∙4∙3)/(3∙2∙1) = 10 ways.\r\n" ); document.write( "\r\n" ); document.write( "That's 4+4+10=18 ways they call all be the same color.\r\n" ); document.write( "\r\n" ); document.write( "That's 18 ways out of 286 or a probability of 18/286 = 9/143\r\n" ); document.write( "\r\n" ); document.write( "------------------------------------------------- \n" ); document.write( "Find the probability that they may be \n" ); document.write( "ii) all of different colors? \r\n" ); document.write( "\r\n" ); document.write( "Choose the red ball any of 4 ways.\r\n" ); document.write( "Choose the white ball any of 4 ways.\r\n" ); document.write( "Choose the green ball any of 5 ways.\r\n" ); document.write( "\r\n" ); document.write( "That's 4∙4∙5 = 80 ways to choose the balls all different colors.\r\n" ); document.write( "\r\n" ); document.write( "That's 80 ways out of 286 or a probability of 80/286 = 40/143\r\n" ); document.write( "\r\n" ); document.write( "Edwin\n" ); document.write( " |