document.write( "Question 879972: Consider a bench on which six student can sit .In how many ways can 3 girls and 3 boys sit on the bench if no girls sit next to one another and also no boys sit next to one another?it is related with permutation and combination \n" ); document.write( "
Algebra.Com's Answer #531167 by josmiceli(19441)\"\" \"About 
You can put this solution on YOUR website!
The way I see it is:
\n" ); document.write( "You can have:
\n" ); document.write( "BGBGBG
\n" ); document.write( "or
\n" ); document.write( "GBGBGB
\n" ); document.write( "----------
\n" ); document.write( "In the 1st case, you have:
\n" ); document.write( "(1) 3 choices for a boy
\n" ); document.write( "(2) 3 choices for a girl
\n" ); document.write( "(3) 2 remaining choices for a boy
\n" ); document.write( "(4) 2 remaining choices for a girl
\n" ); document.write( "(5) 1 remaining choice for a boy
\n" ); document.write( "(6) 1 remaining choice for a girl
\n" ); document.write( "-----------------------------
\n" ); document.write( "In the 2nd case, you have:
\n" ); document.write( "(1) 3 choices for a girl
\n" ); document.write( "(2) 3 choices for a boy
\n" ); document.write( "(3) 2 remaining choices for a girl
\n" ); document.write( "(4) 2 remaining choices for a boy
\n" ); document.write( "(5) 1 remaining choice for a girl
\n" ); document.write( "(6) 1 remaining choice for a boy
\n" ); document.write( "-------------------------------
\n" ); document.write( "Possible seatings total:
\n" ); document.write( "\"+3%2A3%2A2%2A2%2A1%2A1+%2B+3%2A3%2A2%2A2%2A1%2A1+\"
\n" ); document.write( "\"+36+%2B+36+=+72+\"
\n" ); document.write( "72 possible ways\r
\n" ); document.write( "\n" ); document.write( "
\n" ); document.write( "
\n" );