document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=478984>Question 478984</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Ok....You helped answer a question previously and it really helped. Do you think that you can help to explain what I am looking at here and help to apply a formula...I am drawing a blank.<BR>\n" );
document.write( "If you are dealt 4 cards from a shuffled deck of 52 cards, find the probability of getting three aces and one king.<BR>\n" );
document.write( "I serioulsy don't know where to start. Thank you for your time.\r<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #328206 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/cgi-bin/show-face.mpl?user=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=328206\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> you are dealt 4 cards from a deck of 52<BR>\n" );
document.write( "you want to know the probability that you get 3 aces and 1 king.<BR>\n" );
document.write( "there are 4 aces in the deck and there are 4 kings in the deck.<BR>\n" );
document.write( "this is a correction from the last time i issued the answer.  i said 1 king in the deck when i meant 4 kings in the deck.  the rest of the answer was good and assumed the 4 kings in the deck.<BR>\n" );
document.write( "the probability of getting 3 aces and 1 king, without replacement, would be:<BR>\n" );
document.write( "4/52 * 3/51 * 2/50 * 4/49 = .00001448 * 4C1 = .000059101<BR>\n" );
document.write( "using combination theory, the equation would be:<BR>\n" );
document.write( "(4C3 * 4C1) / (52C4) = (4*4)/270725 = 16/270725 = .000059101<BR>\n" );
document.write( "both methods get you the same answer.<BR>\n" );
document.write( "the difference from your other problems is the number of ways the probability can be done.<BR>\n" );
document.write( "the probability method is:<BR>\n" );
document.write( "4/52 * 3/51 * 2/50 * 4/49.<BR>\n" );
document.write( "you are talking about 3 aces and 1 king.<BR>\n" );
document.write( "this could be symbolized as aaak<BR>\n" );
document.write( "you drew 4 cards out of the deck.<BR>\n" );
document.write( "first one was ace, second one was ace, third one was ace, fourth one was king.<BR>\n" );
document.write( "there are 3 other ways this same combination could have been drawn.<BR>\n" );
document.write( "the 4 ways are:<BR>\n" );
document.write( "aaak<BR>\n" );
document.write( "aaka<BR>\n" );
document.write( "akaa<BR>\n" );
document.write( "kaaa<BR>\n" );
document.write( "each one of these configurations has the same probability that is equal to 4/52 * 3/51 * 2/50 * 4/49.<BR>\n" );
document.write( "to account for the fact that you could draw 3 aces and 1 king in 4 different ways, you have to multiply the probability by 4.<BR>\n" );
document.write( "no replacement is assumed here so the 2 methods (probability methods and combination method) should be comparable as they are.<BR>\n" );
document.write( "in the ticket problem, the number of ways was 1 because you were dealing with only tickets.<BR>\n" );
document.write( "in the card problem, the number of ways was 1 because you were dealing with only clubs (same suit).<BR>\n" );
document.write( "your set from the ticket problem was TT<BR>\n" );
document.write( "your set from the club problem was CCC<BR>\n" );
document.write( "either one of these can only happen in one way.<BR>\n" );
document.write( "the problem with the ace and the king was AAAK which, as shown above, could be drawn in 4 ways.\r<BR>\n" );
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