document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1100394>Question 1100394</A>: <I><SPAN STYLE=\"word-break: break-all;\"> In a restaurant, waiters offer 1 toy per meal. If there are 3 assorted toys available, find the probability of getting 3 assorted toys in 5 meals.\r<BR>\n" );
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document.write( "Choices:<BR>\n" );
document.write( "a) 54/243<BR>\n" );
document.write( "b) 45/253<BR>\n" );
document.write( "c) 65/566<BR>\n" );
document.write( "d) 25/324 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #714973 by </B><A HREF=/tutors/aboutme.mpl?userid=greenestamps><B>greenestamps(13203)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=greenestamps><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=greenestamps><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=714973\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br>I'm wondering if you have shown the problem and the answer choices correctly, or if I am misinterpreting the problem.<br><BR>\n" );
document.write( "The answer has to be a fraction with a denominator that is a power of 3, or is a simplified fraction that is equivalent to one with a denominator that is a power of 3.<br><BR>\n" );
document.write( "Based on that, the answer, without doing any calculations, should be a, 54/243.  Note, however, that that is not a good answer choice, since it is a fraction that is not in simplified form.  (54/243 = 2/9).<br><BR>\n" );
document.write( "But the actual calculations -- based on my interpretation of the problem -- don't show that answer.<br><BR>\n" );
document.write( "My interpretation of the problem is we are to find the probability that, in 5 random meals, we get at least one of the 3 available toys.<br><BR>\n" );
document.write( "Based on that interpretation, here are the calculations....<br><BR>\n" );
document.write( "There are two ways to get at least 1 of each toy in 5 meals: (1) we get 3 of 1 toy and 1 of each of the others; or (2) we get 2 each of 2 toys and 1 of the other.<br><BR>\n" );
document.write( "Case (1)...<BR>\n" );
document.write( "If we call the 3 available toys A, B, and C, then we can get either<BR>\n" );
document.write( "AAABC or ABBBC or ABCCC  (3 ways)<BR>\n" );
document.write( "For each of those 3 ways, the number of different orders to get those toys is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%285%21%29%2F%28%283%21%29%281%21%29%281%21%29%29+=+120%2F6+=+20 ALIGN=MIDDLE  ALT=\"%285%21%29%2F%28%283%21%29%281%21%29%281%21%29%29+=+120%2F6+=+20\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "So the total number of ways of getting 3 of 1 toy and 1 each of the other 2 toys in 5 meals is 3*20 = 60.<br><BR>\n" );
document.write( "Case (2)...<BR>\n" );
document.write( "For this case, we can get either<BR>\n" );
document.write( "AABBC or AABCC or ABBCC  (3 ways)<BR>\n" );
document.write( "For each of those 3 ways, the number of different orders to get those toys is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%285%21%29%2F%28%282%21%29%282%21%29%281%21%29%29+=+120%2F4+=+30 ALIGN=MIDDLE  ALT=\"%285%21%29%2F%28%282%21%29%282%21%29%281%21%29%29+=+120%2F4+=+30\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "So the total number of ways of getting 2 each of 2 toys and 1 of the other in 5 meals is 3*30 = 90.<br><BR>\n" );
document.write( "The total number of ways of getting at least 1 of each of the 3 available toys is then 60+90 = 150.<br><BR>\n" );
document.write( "The total number of possible ways of getting 1 of the 3 toys in each of 5 meals is 3^5 = 243.<br><BR>\n" );
document.write( "So the probability of getting at least 1 of each toy in 5 meals is 150/243 = 50/81.<br><BR>\n" );
document.write( "I will be interested to see if you get solutions from any of the other tutors, with the problem interpreted so that 54/243 is the correct answer.... </SPAN>\n" );
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