document.write( "Question 1020210: A garden has 15 slots for flowering pots. In how many ways can the pots be arranged if the garden is circular? \n" ); document.write( "

Algebra.Com's Answer #636135 by mathmate(429) $\"\"$ $\"About$

You can put this solution on YOUR website!

\n" ); document.write( "Question:
\n" ); document.write( "A garden has 15 slots for flowering pots. In how many ways can the pots be arranged if the garden is circular?
\n" ); document.write( "
\n" ); document.write( "Solution:
\n" ); document.write( "We assume from the context of the question that the 15 pots are distinct, or different.
\n" ); document.write( "We further assume that only the ordering of the pots is important, i.e. the positions of the pots have no significance, just like ordering guests at a round table. They can be rotated and still considered the same arrangement.
\n" ); document.write( " \r
\n" ); document.write( "\n" ); document.write( "This way, the position of the first pot is irrelevant. We will position the following pots in the clockwise direction, which gives 14! as the possible number of arrangements.
\n" ); document.write( "
\n" ); document.write( "However, in my personal opinion, the position of the first pot in a garden is important, since a garden is rarely rotationally symmetrical. If that's the case, then there are 15! possible arrangements, taking \"mirror\" arrangements as different. \n" ); document.write( "

\n" );