A survey found that 60% of people prefer apples over oranges, while 40% prefer oranges. If a group of 10 people is randomly selected, what is the probability that exactly 7 people prefer apples and 3 people prefer oranges?
We can solve this problem using the binomial probability formula:

P(x successes in n trials) = C(n, x) * p^x * (1-p)^(n-x)

In this case, "success" means preferring apples, so our parameters are:
- n = 10 (number of people in the group)
- x = 7 (number of people who prefer apples)
- p = 0.6 (probability of preferring apples)

Using these values, we can calculate the probability:

P(7 prefer apples) = C(10, 7) * (0.6)^7 * (1 - 0.6)^(10 - 7)
                              = C(10, 7) * (0.6)^7 * (0.4)^3
                              = 120 * 0.0279936 * 0.064
                              ≈ 0.215

So, the probability that exactly 7 people prefer apples and 3 people prefer oranges in a randomly selected group of 10 is approximately 21.5%.