College bound: In a recent year, the Statistical Abstract of the United States reported that $60 \%$ of students who graduated from high school enrolled in college. Ten high school graduates are sampled. Round the answers to at least four decimal places. Part: $0 / 4$ Part 1 of 4 (a) What is the probability that exactly 6 of them enroll in college? The probability that exactly 6 of them enroll in college is $\square$. Save For Later Submit Assigr Skip Part $\mathrm{Ch}$ Ptworg Certer

Step 1 ：This problem follows a binomial distribution. The probability of success (enrolling in college) is 0.6. We are asked to find the probability of exactly 6 successes in 10 trials.

Step 2 ：The formula for the binomial probability is: \(P(X=k) = C(n, k) \cdot (p^k) \cdot ((1-p)^{n-k})\), where \(P(X=k)\) is the probability of k successes in n trials, \(C(n, k)\) is the combination of n items taken k at a time, p is the probability of success, n is the number of trials, and k is the number of successes.

Step 3 ：Substitute the given values into the formula: n = 10, k = 6, p = 0.6.

Step 4 ：Calculate the combination: \(C(10, 6) = 210\).

Step 5 ：Substitute the values into the formula and calculate the probability: \(P(X=6) = 210 \cdot (0.6^6) \cdot ((1-0.6)^{10-6}) = 0.25082265600000003\).

Step 6 ：Round the answer to at least four decimal places: 0.2508.

Step 7 ：Final Answer: The probability that exactly 6 of them enroll in college is \(\boxed{0.2508}\).