document.write( "Question 1196822: There are 9 people on a basketball team. The probability that you and your two best friends get to stand together in
\n" ); document.write( "the team picture is: \n" ); document.write( "

Algebra.Com's Answer #829825 by ikleyn(52781) $\"\"$ $\"About$

You can put this solution on YOUR website!
.
\n" ); document.write( "There are 9 people on a basketball team. The probability that you and your two best friends
\n" ); document.write( "get to stand together in the team picture is:
\n" ); document.write( "~~~~~~~~~~~~~~~~~\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "

\r\n" );
document.write( "In all, there are 9! different line arrangements on the team picture.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Next, let's calculate the number of all favorable arrangements, where you and two your best friends are together\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "If we consider you and your two best friends as one object, \r\n" );
document.write( "then we have 9-3+1 = 7 objects to arrange.\r\n" );
document.write( "\r\n" );
document.write( "So, we have 7! different arrangements of these 7 objects.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "In addition, there are 3! = 1*2*3 = 6 permutations of the three persons in the small group.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "It gives  6*7! all favorable arrangements.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Finally, the probability, which the problem asks for, is\r\n" );
document.write( "\r\n" );
document.write( "    P =  =  =  = .     ANSWER\r\n" );
document.write( "

\r
\n" ); document.write( "\n" ); document.write( "Solved.\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "

\n" );