probability distribution for 6 fair coins

In a certain experiment, 6 fair coins are flipped. Let the random variable x be the number of heads observed. Construct the probability distribution for the experiment.

The only way i can think to do this may take FOREVER.

Here is my method

1-1-1-1-1-1, 1-2-1-1-1-1, 1-1-2-1-1-1, 1-1-1-2-1-1, 1-1-1-1-2-1, 1-1-1-1-1-2, 1-2-2-1-1-1, 1-1-2-2-1-1, ... 6-6-6-6-6-6

Etc!!!

Is there a more efficient method to create this probability distribuition than listing all (who knows how many) possiblities out?