document.write( "Question 766655: Given a standard deck of 52 cards with 5 cards being dealt to a player.
\n" ); document.write( "(a)find the probability that the player hand will have all 5 cards as spades.
\n" ); document.write( "(b)now find the probability that the player's hand is a flush. Note that a flush is a 5 card poker hand with all 5 cards being the same suit. \n" ); document.write( "
Algebra.Com's Answer #467116 by DrBeeee(684)\"\" \"About 
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First we need to calculate how many 5 card hands that can be dealt from a standard 52 card deck. This is
\n" ); document.write( "(1) 52P5
\n" ); document.write( "However we don't care about the order of the 5 cards so we really want
\n" ); document.write( "(2) 52C5 = 52P5/5!
\n" ); document.write( "Now we need to determine how many of these hands can be all spades. Since there are 13 spades in the deck we can have
\n" ); document.write( "(3) 13P5 and again since order doesn't matter we want
\n" ); document.write( "(4) 13C5 = 13P5/5!
\n" ); document.write( "The probability of being dealt a spade flush is
\n" ); document.write( "(5) P(all spades) = 13P5/5!/(52P5/5!) or
\n" ); document.write( "(6) P(all spades) = 13P5/52P5 or
\n" ); document.write( "(7) P(all spades) = 13*12*11*10*9/(52*51*50*49*48) or after cancellations
\n" ); document.write( "(8) P(all spades) = 11*3/(4*17*5*49*4) or
\n" ); document.write( "(9) P(all spades) = 33/66640
\n" ); document.write( "Answer to a) is P(flush in spades) = 33/66640
\n" ); document.write( "For the second question, \"any flush\" is 4 times as probable than that of one of the four suits, therefore the
\n" ); document.write( "Answer to b) is P(flush in any suit) = 33/16660 \n" ); document.write( "
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