Here is one method. I started with this input file that includes some repeat lines:
cat tupl
11 12 11 44 11 12 11 23
12 21 11 44 11 12 11 23
12 21 11 44 11 12 11 23
12 21 11 44 11 12 11 23
12 21 11 44 11 12 11 23
11 42 21 13 12 21 31 14
11 42 21 13 12 21 11 34
11 12 11 44 11 12 11 23
Since you say the order of numbers in each row is unimportant we can sort numbers of each row first:
awk ' {split( $0, a, " " ); asort( a ); for( i = 1; i <= length(a); i++ ) printf( "%s ", a[i] ); printf( "\n" ); }' tupl
11 11 11 11 12 12 23 44
11 11 11 12 12 21 23 44
11 11 11 12 12 21 23 44
11 11 11 12 12 21 23 44
11 11 11 12 12 21 23 44
11 12 13 14 21 21 31 42
11 11 12 13 21 21 34 42
11 11 11 11 12 12 23 44
Now you can use the associative arrays idea of awk to count identical rows by piping that result into this command:
awk '{a[$0]++} END {for (i in a) print i, a[i]}'
11 12 13 14 21 21 31 42 1
11 11 11 11 12 12 23 44 2
11 11 12 13 21 21 34 42 1
11 11 11 12 12 21 23 44 4