document.write( "Question 1016237: how many possible ways can be drawn on a flush? \n" ); document.write( "
Algebra.Com's Answer #632705 by Edwin McCravy(20055)![]() ![]() You can put this solution on YOUR website! \r\n" ); document.write( "A flush is 5 cards of the same suit. I don't know if\r\n" ); document.write( "you want to consider a straight flush as a flush or not.\r\n" ); document.write( "\r\n" ); document.write( "Choose the suit for the flush 4 ways.\r\n" ); document.write( "Choose the ranks: 13 cards choose 5. That's 13C5 \r\n" ); document.write( "\r\n" ); document.write( "Answer: 4*(13C5) = 4(1287) = 5148 \r\n" ); document.write( "\r\n" ); document.write( "There are 5148 possible flushes, including straight flushes.\r\n" ); document.write( "\r\n" ); document.write( "Straight flushes can be a set of any of these 10\r\n" ); document.write( "\r\n" ); document.write( "{A,2,3,4,5}\r\n" ); document.write( "{2,3,4,5,6}\r\n" ); document.write( "{3,4,5,6,7}\r\n" ); document.write( "{4,5,6,7,8}\r\n" ); document.write( "{5,6,7,8,9}\r\n" ); document.write( "{6,7,8,9,10}\r\n" ); document.write( "{7,8,9,10,J}\r\n" ); document.write( "{8,9,10,J,Q}\r\n" ); document.write( "{9,10,J,Q,K}\r\n" ); document.write( "{10,J,Q,K,A}\r\n" ); document.write( "\r\n" ); document.write( "There are 4 suits that each could be, so\r\n" ); document.write( "there are 10*4 = 40 straight flushes.\r\n" ); document.write( "\r\n" ); document.write( "So the answer is 5148 if you are counting straight flushes,\r\n" ); document.write( "but only 5148-40 = 5108 if you are not \r\n" ); document.write( "\r\n" ); document.write( "Edwin\n" ); document.write( " |