Runners in a marathon are randomly assigned to one of ten corrals to start, and each given a green, blue, or red shirt to wear.

Counting principle to find number of outcomes.

For each runner we have two selections:

the corrals where they start, we have 10 of them.

The color of the shirt, we have 3 colours.

Then the possible outcomes for each runner is the product between those two number of options:

Outcomes for each runner = 3*10 = 30

Now, if we have 10 different runners. such that we assign one of them to each one of the corrals, we have that in the first corral we can put 1 of the 10 runners.

In the second corral we can put 1 of the 9 runners left (9 because we already take one)

For the third one we need to select between 8 runners, etc

And so on.

Then the number of possible outcomes is:

C = 10*9*8*7*6*5*4*3*2*1

And remember that for each one of these 10 runners, we have 3 possible colours of shirts, so we need to write this as:

C = (10*3) * (9*3) * (8*3) (7*3) * (6*3) * (5*3) * (4*3) * (3*3) * (2*3) * (1*3)

C = 10! * (3^10) = 214,277,011,200

So in this case we have a lot of possible combinations.