I play the lottery and got into an argument with a friend about random numbers. In the Mega Millions game, five balls come out (forget the extra yellow one) with numbers from 1 to 56. Now let’s say 1, 2, 3, 4, 5 come out. That doesn’t look very random, compared with 55, 54, 28, 11, 44. Are these equally likely combinations?
This is actually a pretty deep question. Either of the two is an equally likely outcome, and there’s no way ahead of the draw to imagine how you would prefer one over the other, so both outcomes are random (unpredictable before the fact).
That said, the first set of numbers does somehow look less random, but what does that really mean? It’s just psychological - the sequence 1, 2, 3, 4, 5 is meaningful to you because that is how we count, so it looks like something special.
On the other hand, if your phone number were 555-428-1144, the sequence 55, 54, 28, 11, 44 would look anything but random, and you would think to yourself that this was an amazing coincidence.
It might help to forget about the meaning (to humans) of numbers and think of them as arbitrary symbols to make each ball distinct. In place of 1 you could have had a picture of a pair of pliers, and in place of 2 an orange-colored pickle, and so on.
Now it’s easy to see that all possible sequences are equally likely, and any outcome would have to be judged as a random one, even though the symbols may mean something to you or to some other person.
An alien with no knowledge of how we write numbers would not find either outcome significant - he or she (or it) would just see five balls with distinct markings.
The notion of meaning is a human one, and the apparently amazing quality of a given outcome simply reflects how unlikely it is that, given some random sequence, you would find it meaningful. All the sequences are random.
Ask Dr. Knowledge is written by a Northeastern University physicist, John Swain. E-mail questions to drknowledge@globe.com or write to Dr. Knowledge, c/o The Boston Globe, PO Box 55819, Boston, MA 02205-5819. 
