document.write( "Question 1189667: (1) \r
\n" ); document.write( "\n" ); document.write( "(2) How many different ways can 3 red, 4 yellow and 2 blue bulbs be arranged in a string of Christmas tree lights with 9 sockets?\r
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Algebra.Com's Answer #821126 by ikleyn(52781) $\"\"$ $\"About$

You can put this solution on YOUR website!
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\n" ); document.write( "\n" ); document.write( " Of the three different problems posted, I will solve the second one, ONLY.\r
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document.write( "The total number of sockets is 9.\r\n" );
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document.write( "There are   =  = 84 different ways to select 3 sockets from 9 sockets for 3 red bulbs.\r\n" );
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document.write( "There are   =  = 15 different ways to select 4 sockets from 9-3 = 6 remaining sockets for 4 yellow bulbs.\r\n" );
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document.write( "After that, the sockets for remaining 2 blue bulbs are the remaining 2 sockets, so there is only 1 way to place them (there is no other choice).\r\n" );
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document.write( "In all, there are 84*15 = 1260 ways to arrange the bulbs, according to the Fundamental counting principle.    ANSWER\r\n" );
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\n" ); document.write( "\n" ); document.write( " There is another method to solve the problem.\r
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document.write( "Among 9 bulbs, we have 3 indistinguishable red bulbs; 4 indistinguishable yellow bulbs and 2 indistinguishable blue bulbs.\r\n" );
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document.write( "So, we apply the formula for distinguishable/indistinguishable permutations and find the number of distinguishable arrangements\r\n" );
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document.write( "     = 1260,\r\n" );
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document.write( "which gives the same answer.\r\n" );
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\n" ); document.write( "\n" ); document.write( "Solved by two different methods, giving the same answer.\r
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\n" ); document.write( "\n" ); document.write( "To learn the subject, see my lessons\r
\n" ); document.write( "\n" ); document.write( "    - Introduction to Combinations\r
\n" ); document.write( "\n" ); document.write( "    - PROOF of the formula on the number of Combinations\r
\n" ); document.write( "\n" ); document.write( "    - Problems on Combinations\r
\n" ); document.write( "\n" ); document.write( "    - Fundamental counting principle problems \r
\n" ); document.write( "\n" ); document.write( "    - Arranging elements of sets containing indistinguishable elements \r
\n" ); document.write( "\n" ); document.write( "in this site.   Find there many other similar and different solved problems.\r
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\n" ); document.write( "\n" ); document.write( "Here I explain, why I solved only one problem and ignored two others.\r
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\n" ); document.write( "\n" ); document.write( "It is because the rules of this forum PROHIBIT posting more than one problem per post.\r
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\n" ); document.write( "\n" ); document.write( "Why it is so ? - - - BECAUSE this forum's task and profile is to TEACH.\r
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\n" ); document.write( "\n" ); document.write( "          When a person/(a visitor) posts more than one problem per post,
\n" ); document.write( "        it means only one thing :   his or her goal is everything except of learning.\r
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\n" ); document.write( "\n" ); document.write( "About the rules and the policy of this forum read at this web-page\r
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\n" ); document.write( "\n" ); document.write( "https://www.algebra.com/tutors/students/ask.mpl?action=ask_question&topic=Equations&return_url=http://www.algebra.com/algebra/homework/equations/\r
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\n" ); document.write( "\n" ); document.write( "from which you post your problems.\r
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\n" ); document.write( "\n" ); document.write( "It is assumed that you read these rules before posting.\r
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\n" ); document.write( "\n" ); document.write( "It is also assumed that you do understand what is written in that page and follow the rules.\r
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\n" ); document.write( "\n" ); document.write( "Those who violate them, work against their own interests.\r
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\n" ); document.write( "\n" ); document.write( "        So   P L E A S E   post your problems   S E P A R A T E L Y (!)\r
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