You could use a reservoir sampling algorithm (see also perldoc -q random) :

#!/usr/bin/env perl

my $k = shift @ARGV;
srand;
while (<>) {
    $. <= $k and do { push @lines, $_; next; };
    ($a=rand($.)) < $k and ($lines[$a] = $_);
}
print @lines;
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For instance,

$ seq 4 20 | ./rand.pl 8
19
5
6
14
16
9
15
11
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