@filetoread = <INFILE>;            # read in file all at once
my $linestooutput = '';            # place to save output until the end
foreach (@filetoread){
    @Line = split /\s+/;  #split defaults to $_
    $linestooutput .= join("\t",@Line[@ColumnNumbers])."\n"; 
}
print OUTFILE $linestooutput;      # write output

# or even shorter
@filetoread = <INFILE>;
$linestooutput .= join("\t",(split /\s+/)[@ColumnNumbers])."\n" foreach (@filetoread); 
print OUTFILE $linestooutput;


##</code><code>##

while(<INFILE>)
{
    # get the current line and split into it's columns
    @Line = split /\s+/, $_;

    #print the selected columns to the output
    my $outline .= @Line[$col]."\t" foreach my $col (@ColumnNumbers);
    print OUTFILE $outline,"\n";
}