Another Perl variant, using List::Util
$ perl -MList::Util=uniq -alne '
map { $h{$_}++ } uniq @F }{ for $k (sort keys %h) {print "$k: $h{$k}"}
' file
0: 1
1: 1
2: 1
a: 1
different: 1
hello: 1
is: 3
man: 2
one: 1
possible: 1
the: 3
this: 1
world: 2