#!/usr/bin/perl

use strict;

my %chosen; # you don't need a 10-element array to draw from

while ( keys %chosen < 3 ) {
    my $pick = int( rand(10)) + 1;
    $chosen{$pick} = undef;
}

print join " ", keys %chosen, "\n";

# (you could "sort {$a<=>$b) keys %chosen", if that matters)