Pick N distinct items at random from sequence of unknown length, in only one iteration

I am trying to write an algorithm that would pick N distinct items from an sequence at random, without knowing the size of the sequence in advance, and where it is expensive to iterate over the sequence more than once. For example, the elements of the sequence might be the lines of a huge file.

I have found a solution when N=1 (that is, "pick exactly one element at random from a huge sequence"):

import random
items = range(1, 10) # Imagine this is a huge sequence of unknown length
count = 1
selected = None
for item in items:
    if random.random() * count < 1:
        selected = item
    count += 1

But how can I achieve the same thing for other values of N (say, N=3)?

Use reservoir sampling. It's a very simple algorithm that works for any N.

Here is one Python implementation, and here is another.