document.write( "Question 1206919: One artist donates 3 different sculptures and 6 different vases to the museum. The exhibits will be arranged in a row. Find the number of possible arrangements if each sculpture must be placed between two vases. \n" ); document.write( "

Algebra.Com's Answer #844642 by ikleyn(52781) $\"\"$ $\"About$

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\n" ); document.write( "One artist donates 3 different sculptures and 6 different vases to the museum.
\n" ); document.write( "The exhibits will be arranged in a row. Find the number of possible arrangements
\n" ); document.write( "if each sculpture must be placed between two vases.
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document.write( "The sculptures are placed in the gaps between the vases.\r\n" );
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document.write( "In all, there are 6 different vases and 6-1 = 5 gaps between them.\r\n" );
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document.write( "Of these 5 gaps, we can select 3 gaps to place sculptures by   =  = 5*2 = 10 different ways.\r\n" );
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document.write( "So, we have 10 different options to choose 3 gaps for sculptures;\r\n" );
document.write( "3! = 6 ways to order these 3 sculptures (permutations of 3 objects),\r\n" );
document.write( "and 6! = 720 ways to order 6 vases (permutations of 6 objects).\r\n" );
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document.write( "Thus, in all, there are 10*6*720 = 43200 different arrangements.    ANSWER\r\n" );
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