document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=88339>Question 88339</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I need help understanding how to solve these problems....can someone explain them to me...\r<BR>\n" );
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document.write( "1) How many 5-card poker hands consisting of 2 aces and 3 kings are possible with an ordinary 52-card deck?\r<BR>\n" );
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document.write( "2) A bag contains 5 apples and 3 oranges. If you select 4 pieces of fruit without looking, how many ways can you get exactly 3 apples?\r<BR>\n" );
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document.write( "3) How many different three-number \"combinations\" are possible on a combination lock having 24 numbers on its dial? Assume that no numbers repeat. (combination locks are really permutation locks)\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 #64260 by </B><A HREF=/tutors/aboutme.mpl?userid=stanbon><B>stanbon(75887)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=stanbon><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=64260\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> 1) How many 5-card poker hands consisting of 2 aces and 3 kings are possible with an ordinary 52-card deck? <BR>\n" );
document.write( "# or ways to pick 2 aces out of 4 = 4C2 = 6<BR>\n" );
document.write( "# of ways to pick 3 kings out of 4 is 4C3 = 4<BR>\n" );
document.write( "# of ways to pick a 5 card hand out of 52 card = 52C5<BR>\n" );
document.write( "P(2 aces and 3 kings) = [6*4]/52C5 = 0.0000092344<BR>\n" );
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document.write( "2) A bag contains 5 apples and 3 oranges. If you select 4 pieces of fruit without looking, how many ways can you get exactly 3 apples? <BR>\n" );
document.write( "# of ways to pick 3 apples = 5C3 = [5*4*3]/[1*2*3] = 10<BR>\n" );
document.write( "# of ways to get the orange = 3C1 = 3 ways<BR>\n" );
document.write( "# of ways to get exactly 3 apples when pick 4 of the fruit is 10*3=30<BR>\n" );
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document.write( "3) How many different three-number \"combinations\" are possible on a combination lock having 24 numbers on its dial? Assume that no numbers repeat. (combination locks are really permutation locks)<BR>\n" );
document.write( "The number of combination s 24C3 = 2024<BR>\n" );
document.write( "Since a lock combination depends on the order of the numbers you have to multiply by 3!=6<BR>\n" );
document.write( "So, number of combinations is 6*2024 = 12144<BR>\n" );
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document.write( "You could get the same answer by thinking the following:<BR>\n" );
document.write( "24 ways to pick the 1st number<BR>\n" );
document.write( "23 ways to pick the 2nd number<BR>\n" );
document.write( "22 ways to pick the 3rd number<BR>\n" );
document.write( "Total way = 24*23*22 = 12144<BR>\n" );
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document.write( "This is the same as 24P3=12144<BR>\n" );
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document.write( "Cheers,<BR>\n" );
document.write( "Stan H.\r<BR>\n" );
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