document.write( "Question 1153490: There are 16 students giving final presentations in your history course.\r
\n" ); document.write( "\n" ); document.write( "(a) Three students present per day. How many presentation orders are possible for the first day?\r
\n" ); document.write( "\n" ); document.write( "(b) Presentation subjects are based on the units of the course. Unit B is covered by three students, Unit C is covered by five students, and Units A and D are each covered by four students. How many presentation orders are possible when presentations on the same unit are indistinguishable form each other? \n" ); document.write( "

Algebra.Com's Answer #775738 by ikleyn(52781) $\"\"$ $\"About$

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document.write( "(a)  \"How many presentation orders are possible for the first day\" = 16*15*14.\r\n" );
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document.write( "     Any of 16 students can give 1-st presentation.\r\n" );
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document.write( "     Any of remaining 15 students can give 2-nd presentation.\r\n" );
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document.write( "     Any of remaining 14 students can give 3-rd presentation.\r\n" );
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document.write( "     The total is the product of these factors.\r\n" );
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document.write( "(b)  The number of orders in this case is\r\n" );
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document.write( "         N =  = 50450400.\r\n" );
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document.write( "     This formula is standard for such kind of problems on arranging the set containing groups of indistinguishable elements.\r\n" );
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document.write( "     The factorials in denominator serve to account multiplicities of indistinguishable elements in groups.\r\n" );
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document.write( "     Probably, it would be more clear, if I retell it in other way.\r\n" );
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document.write( "     We may think that each of 16 students simply carries the name of the unit \"A\", \"B\", \"C\" and \"D\",\r\n" );
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document.write( "     instead of making real presentation.\r\n" );
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document.write( "     Then the question is: how many 16-letter words do exist, written in  4-letter alphabet A, B, C and D, in a way that\r\n" );
document.write( "      letter A occurs 4 times; letter B occurs 3 times; letter C occurs 5 times, and letter D occurs 4 times.\r\n" );
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document.write( "     Then the answer to this question is EXACTLY as I described it above. \r\n" );
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\n" ); document.write( "\n" ); document.write( "Solved, answered and explained. And completed.\r
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\n" ); document.write( "\n" ); document.write( "To see other similar solved problems, look into the lesson\r
\n" ); document.write( "\n" ); document.write( " - Arranging elements of sets containing indistinguishable elements \r
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\n" ); document.write( "\n" ); document.write( "Also, you have this free of charge online textbook in ALGEBRA-II in this site\r
\n" ); document.write( "\n" ); document.write( " - ALGEBRA-II - YOUR ONLINE TEXTBOOK.\r
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\n" ); document.write( "\n" ); document.write( "The referred lessons are the part of this online textbook under the topic \"Combinatorics: Combinations and permutations\". \r
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\n" ); document.write( "\n" ); document.write( "Save the link to this textbook together with its description\r
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\n" ); document.write( "\n" ); document.write( "Free of charge online textbook in ALGEBRA-II
\n" ); document.write( "https://www.algebra.com/algebra/homework/complex/ALGEBRA-II-YOUR-ONLINE-TEXTBOOK.lesson\r
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\n" ); document.write( "\n" ); document.write( "into your archive and use when it is needed.\r
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