document.write( "Question 1195311: How many ways can 2 purple, 3 yellow, and 2 blue bulbs be arranged in a string of Christmas tree lights with 7 socks? \n" ); document.write( "
Algebra.Com's Answer #827772 by ikleyn(52803)\"\" \"About 
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\n" ); document.write( "How many ways can 2 purple, 3 yellow, and 2 blue bulbs be arranged in a string
\n" ); document.write( "of Christmas tree lights with 7 socks?
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document.write( "This problem is about arranging a line of objects, \r\n" );
document.write( "where distinguishable/undistinguishable objects/items are.\r\n" );
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document.write( "Use the formula for it\r\n" );
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document.write( "    the number of distinguishable arrangements = \"%282%2B3%2B2%29%21%2F%282%21%2A3%21%2A2%21%29\"\r\n" );
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document.write( "where 2+3+2 = 7 is the total number of objects, and 2, 3 and 2 are the \"multiplicities\" \r\n" );
document.write( "of undistinguishable object.\r\n" );
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document.write( "The formula gives\r\n" );
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document.write( "    the number of distinguishable arrangements = \"7%21%2F%282%21%2A3%21%2A2%21%29\" = \"%281%2A2%2A3%2A4%2A5%2A6%2A7%29%2F%28%281%2A2%29%2A%281%2A2%2A3%29%2A%281%2A2%29%29\" = \"5040%2F%282%2A6%2A2%29\" = \"5040%2F24\" = 210.\r\n" );
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document.write( "ANSWER.  There are 210 distinguishable arrangements.\r\n" );
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\n" ); document.write( "\n" ); document.write( "Solved, answered and explained.\r
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\n" ); document.write( "\n" ); document.write( "To see many other similar  (and different)  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 lesson is 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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