In how many ways can a picture be painted by using two or more of 7 different
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document.write( "We will do each of those separately:\r\n" );
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document.write( "For each of those 7 colors, there are exactly 2 decisions we can make\r\n" );
document.write( "concerning that color. They are:\r\n" );
document.write( "(1) Use it in the picture.\r\n" );
document.write( "(2) Don't use it in the picture.\r\n" );
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document.write( "Suppose the 7 colors are R,O,Y,G,B,I,V.\r\n" );
document.write( "There are 2 decisions we can make about color R.\r\n" );
document.write( "For each of those, there are 2 decisions we can make about color O.\r\n" );
document.write( "For each of those, there are 2 decisions we can make about color Y.\r\n" );
document.write( "For each of those, there are 2 decisions we can make about color G.\r\n" );
document.write( "For each of those, there are 2 decisions we can make about color B.\r\n" );
document.write( "For each of those, there are 2 decisions we can make about color I.\r\n" );
document.write( "For each of those, there are 2 decisions we can make about color V.\r\n" );
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document.write( "That's 2∙2∙2∙2∙2∙2∙2 = 27 = 128 ways.\r\n" );
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document.write( "This one is easy because there is just 1 way to say \"no\" to all 7 colors,\r\n" );
document.write( "and that 1 way is to say \"no\" to all of them. (That is we paint the picture\r\n" );
document.write( "in black and white, using NO colors).\r\n" );
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document.write( "That's 1 way.\r\n" );
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document.write( "This one is also easy because there are 7 colors we can choose to\r\n" );
document.write( "say \"yes\" to (saying \"no\" to each the other 6 colors)\r\n" );
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document.write( "That's 7 ways.\r\n" );
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document.write( "So:\r\n" );
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document.write( "Edwin
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