document.write( "Question 798821: number of ways of selecting 4 men from the row of 10 men such that no two are adjacent to each other \n" ); document.write( "
Algebra.Com's Answer #482377 by Finavon(81)\"\" \"About 
You can put this solution on YOUR website!
1 3 5 7 or 8 or 9 or 10
\n" ); document.write( "1 3 6 8 or 9 or 10
\n" ); document.write( "1 3 7 9 or 10
\n" ); document.write( "1 3 8 10
\n" ); document.write( "1 4 6 8 or 9 or 10
\n" ); document.write( "1 4 7 9 or 10
\n" ); document.write( "1 4 8 10
\n" ); document.write( "1 5 7 9 or 10
\n" ); document.write( "1 5 8 10
\n" ); document.write( "1 6 8 10
\n" ); document.write( "2 4 6 8 or 9 or 10
\n" ); document.write( "2 4 7 9 or 10
\n" ); document.write( "2 4 8 10
\n" ); document.write( "2 5 7 9 or 10
\n" ); document.write( "2 5 8 10
\n" ); document.write( "2 6 8 10
\n" ); document.write( "3 5 7 9 or 10
\n" ); document.write( "3 5 8 10
\n" ); document.write( "3 6 8 10
\n" ); document.write( "4 6 8 10\r
\n" ); document.write( "\n" ); document.write( "Count 35 combinations (order ignored)\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "If order matters :
\n" ); document.write( "For each combination:
\n" ); document.write( "A B C D
\n" ); document.write( "A B D C
\n" ); document.write( "A C B D
\n" ); document.write( "A C D B
\n" ); document.write( "A D B C
\n" ); document.write( "A D C B
\n" ); document.write( "Any one of the group of 4 can be first
\n" ); document.write( "with 6 permutations of the remaining 3
\n" ); document.write( "so 4x6 = 24 permutations of each combination.
\n" ); document.write( "Overall 24 x 35 = 840 permutations \n" ); document.write( "
\n" );