document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1098385>Question 1098385</A>: <I><SPAN STYLE=\"word-break: break-all;\"> a. How many ways are there to choose four fives from a standard 52-card deck?<BR>\n" );
document.write( "b. How many ways are there to choose one card from a standard 52-card deck without choosing any fives?<BR>\n" );
document.write( "c. How many five-card hands (drawn from a standard 52-card deck) contain exactly four fives?<BR>\n" );
document.write( "d. How many five-card hands (drawn from a standard 52-card deck) contain a four-of-a-kind? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #713202 by </B><A HREF=/tutors/aboutme.mpl?userid=KMST><B>KMST(5328)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=KMST><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=KMST><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=713202\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> a. How many ways are there to choose four fives from a standard 52-card deck?<BR>\n" );
document.write( "There are only 4 fives, so there is only 1 possible set of fives you can get..<BR>\n" );
document.write( "There is only 1 such combination, and that is what I believe was meant by the question.<BR>\n" );
document.write( "(If you cared what order the cards were received, there would be 4!=4*3*2=24 permutataions).<BR>\n" );
document.write( " <BR>\n" );
document.write( "b. How many ways are there to choose one card from a standard 52-card deck without choosing any fives?<BR>\n" );
document.write( "52-4=48 of the cards are not a five,<BR>\n" );
document.write( "so there are 48 ways to choose one card from a standard 52-card deck without choosing any five.<BR>\n" );
document.write( " <BR>\n" );
document.write( "c. How many five-card hands (drawn from a standard 52-card deck) contain exactly four fives?<BR>\n" );
document.write( "As there is exactly 1 set of 4 fives, and 48 ways to choose the 5th card,<BR>\n" );
document.write( "there are 1 X 48 = 48 five-card hands containing exactly four fives.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "d. How many five-card hands (drawn from a standard 52-card deck) contain a four-of-a-kind?<BR>\n" );
document.write( "There are 52/4=13 different \"kinds of cards in a standard 52-card deck.<BR>\n" );
document.write( "There are 48 five-card hands containing exactly four fives.<BR>\n" );
document.write( "There are also<BR>\n" );
document.write( "48 five-card hands containing exactly four aces,<BR>\n" );
document.write( "48 five-card hands containing exactly four twos,<BR>\n" );
document.write( "48 five-card hands containing exactly four threes,<BR>\n" );
document.write( "48 five-card hands containing exactly four fours,<BR>\n" );
document.write( "48 five-card hands containing exactly four sixes,<BR>\n" );
document.write( "and so on.<BR>\n" );
document.write( "Considering all 13 kinds of cards there are 13 X 48 = 624<BR>\n" );
document.write( "card hands containing four-of-a-kind.<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );