Question

After analyzing the data, the campaign team decide to recruit a random selection of 9 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.

How many total focus groups could possibly be formed?

Answer 1

The campaign team can form a total of 1,731,030,945 unique focus groups by selecting 9 respondents from 1020 potential candidates. The combinations formula from mathematics is used for this calculation.

Step-by-step explanation:

The total number of possible focus groups that can be formed from 1020 respondents by selecting 9 at a time is 1,731,030,945 focus groups. This calculation is based on the combinations formula, which in mathematics is used to find the number of ways a certain number of items can be chosen from a larger group without regard to the order in which they are selected.

To calculate the number of possible combinations for the focus group, you would use the formula for combinations: C(n, k) = n! / (k!(n-k)!), where 'n' represents the total number of items to choose from, 'k' represents the number of items to choose, '! stands' for factorial, and C(n, k) represents the number of combinations possible.

In this case, 'n' is 1020 (the total number of respondents), and 'k' is 9 (the number of respondents to be chosen for each focus group). Using the formula, we find that C(1020, 9) is the total number of distinct groups that can be formed, which equals 1,731,030,945.