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