document.write( "Question 1175421: Nine cards, all in a different colour, 3 cards are selected from the 9 cards and arranged in a line. How many different possible arrangements of 3 selected cards do not have the pink card next to the green card? \n" ); document.write( "

Algebra.Com's Answer #801030 by ikleyn(52781) $\"\"$ $\"About$

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\n" ); document.write( "Nine cards, all in a different colour, 3 cards are selected from the 9 cards and arranged in a line.
\n" ); document.write( "How many different possible arrangements of 3 selected cards do not have the pink card next to the green card?
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document.write( "In all, there are 9*8*7 = 504  different possible arrangements of 9 different object \r\n" );
document.write( "(colored cards, in this case), taken 3 at a time.\r\n" );
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document.write( "From this number, we should subtract those unwanted arrangements, where pink is next to green card.\r\n" );
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document.write( "The number of such unwanted arrangements is  2*2*7 = 28 (there are 2 possible positions for such pair of cards \r\n" );
document.write( "in the short line of 3 positions;  there are 2 ways to order these 2 card (pink/green or green/pink) \r\n" );
document.write( "and there are 7 ways to supplement these two cards by the third card.\r\n" );
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document.write( "So, the final answer is: the number of ways is  9*8*7 - 2*2*7 = 504 - 28 = 476.\r\n" );
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