Final answer:
There are 6 different combinations of activities that the campers can choose for the first day of camp.
Step-by-step explanation:
To find the number of different combinations of activities, we can use the concept of combinations. Since the campers can choose two activities from a pool of four activities, we can use the formula for combinations to find the answer. The formula for combinations is nCr = n! / (r! * (n-r)!), where n is the total number of activities and r is the number of activities being chosen.
In this case, n = 4 (the total number of activities) and r = 2 (since the campers choose two activities). Plugging these values into the formula, we get:
nCr = 4! / (2! * (4-2)!) = 4! / (2! * 2!) = (4 * 3 * 2 * 1) / ((2 * 1) * (2 * 1)) = 24 / 4 = 6
So, there are 6 different combinations of activities that the campers can choose for the first day of camp.