Any time you see code that is almost the same, except for variable names or constants, make it the same:

sub get_random_line
{
    my $filename = shift;
    open my $fh, '<', $filename or die "Cannot read '$filename': $!\n"
+;
    return random_line( $fh );
}

my $filename;

if (my $cut =~ /[a-e]/i)
{
    $filename = 'infinity01.txt'
}
elsif ( ... )
{
   ...
}

my $random_line = get_random_line( $filename );
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