document.write( "Question 846651: A poker hand consists of five cards from a standard deck of 52. (See the chart preceding Example 8.) Find the number of different poker hands of the specified type. HINT [See Example 8.]
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Algebra.Com's Answer #512042 by Edwin McCravy(20055)\"\" \"About 
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A poker hand consists of five cards from a standard deck of 52. (See the chart preceding Example 8.) Find the number of different poker hands of the specified type. HINT [See Example 8.]
\n" ); document.write( "Straight (five cards of consecutive denominations: A, 2, 3, 4, 5 up through 10, J, Q, K, A, not all of the same suit) (Note that the ace counts either as a 1 or as the denomination above king.)
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document.write( "There are 10 different types of straights or straight flushes:\r\n" );
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document.write( " 1. A,2,3,4,5\r\n" );
document.write( " 2. 2,3,4,5,6\r\n" );
document.write( " 3. 3,4,5,6,7\r\n" );
document.write( " 4. 4,5,6,7,8\r\n" );
document.write( " 5. 5,6,7,8,9\r\n" );
document.write( " 6. 6,7,8,9,10\r\n" );
document.write( " 7. 7,8,9,10,J\r\n" );
document.write( " 8. 8,9,10,J,Q\r\n" );
document.write( " 9. 9,10,J,Q,K\r\n" );
document.write( "10. 10,J,Q,K,A\r\n" );
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document.write( "We can choose the type of straight or straight flush from \r\n" );
document.write( "the above list 10 ways.\r\n" );
document.write( "We can choose the suit for the lowest card 4 ways.\r\n" );
document.write( "We can choose the suit for the next to lowest card 4 ways.\r\n" );
document.write( "We can choose the suit for the middle card 4 ways.\r\n" );
document.write( "We can choose the suit for the next to highest card 4 ways.\r\n" );
document.write( "We can choose the suit for the highest card 4 ways.\r\n" );
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document.write( "That is 10×4×4×4×4×4 = 10×45 = 10240 straights or straight flushes.\r\n" );
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document.write( "But we must subtract from that the number of straight flushes,\r\n" );
document.write( "where they are all of the same suit.\r\n" );
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document.write( "So we calculate the number of straight flushes:\r\n" );
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document.write( "There are 10 types of straight flushes.\r\n" );
document.write( "There are 4 suits each type can have.\r\n" );
document.write( "So there are 10×4 or 40 possible straight flushes.\r\n" );
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document.write( "So there are 10240 - 40 or 10200 possible straights.\r\n" );
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document.write( "Edwin
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