document.write( "Question 1206918: An artist donates 3 different sculptures and 6 different vases to a museum. The exhibits will be arranged in a row. Find the number of possible arrangements if (a.) The 3 sculptures are placed together. (b.) The 3 sculptures are placed in the middle. (c.) Each sculpture must be placed between two vases. \n" ); document.write( "
Algebra.Com's Answer #844653 by Edwin McCravy(20055)\"\" \"About 
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document.write( "(a.) \r\n" );
document.write( "SSSVVVVVV, VSSSVVVVV, VVSSSVVVV, VVVSSSVVV, VVVVSSSVV, VVVVVSSSV, VVVVVVSSS\r\n" );
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document.write( "As you see above, there are 7 ways to put 0,1,...,6 V's before the 3 S's.\r\n" );
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document.write( "For each of those 7 ways, there are 6! ways to arrange the V's and 3! ways to\r\n" );
document.write( "arrange the S's.  That's (7)(6!)(3!) = 30240 ways. \r\n" );
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document.write( "(b.) That's just 1/7 of the above, the case VVVSSSVVV, (6!)(3!) = 4320.\r\n" );
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document.write( "(c.) V_V_V_V_V_V\r\n" );
document.write( "We can arrange the V's in 5! ways. Label the sculptures S1, S2, S3\r\n" );
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document.write( "For each of those 5! ways, we choose \r\n" );
document.write( "1. a blank to place S1 in 5 ways.\r\n" );
document.write( "2. a blank to place S2 in 4 ways.\r\n" );
document.write( "3. a blank to place S3 in 3 ways.\r\n" );
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document.write( "That's (6!)(5)(4)(3) = 43200 ways.\r\n" );
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document.write( "Edwin

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