6. Counting Categories In each part below, remember to explain your answer. Don't just write down a formula. You don't have to provide decimal answers. Note: See the video right at the bottom of Section 5.4 (below the last Quick Check) for an effective approach. A population consists of 6 individuals in each of 4 categories A, B, C, and D. A simple random sample of 12 individuals is chosen from the population. a) Find the chance that the sample contains equal numbers of individuals in the four categories. b) Find the chance that the sample contains 5 individuals in one category, 4 in another, 2 in a third, and 1 in the remaining category. c) Find the chance that the sample contains 4 individuals in each of two categories, 3 individuals in another, and 1 in the remaining category. d) Find the chance that the sample contains all 6 individuals in one category and equal numbers in the other three. #newpage