4. After analyzing the data, the campaign team decide to recruit a random selection of 7 respondents of the 1020 to participate in a focus group. The team hopes to collect more personalized data on opinions of their candidate, political leanings, issues that people in the community care about, etc.

(a) [5 points] How many total focus groups could possibly be formed?

(b) [5 points] Suppose that 597 of the respondents identified as Caucasian, 295 as African Amer- ican, 48 as Hispanic, 43 as Asian, and37 identified as other. Find the probability of forming a focus group with at least two non-Caucasian persons. Include any decision algorithms used in obtaining your answer.

(c) [5 points] Suppose that 540 of the respondents identified as women, 438 identified as male, and 42 identified as other or non-binary. What is the probability of forming a focus group with two females, two males, two other or non-binary persons, and one additional person from any of the previous three groups? Include any decision algorithms used in obtaining your answer.

Hint: Think about the possible outcomes for the additional person when designing your de- cision algorithm.

(d) [5 points] Why might the campaign team care about the calculations obtained in parts (b)-(c)?