Final answer:
To form a committee of 2 Republicans and 2 Democrats, first calculate the combinations separately using the formula nCk, and then multiply them together. There are 55 ways to choose 2 Republicans from 11 and 36 ways to choose 2 Democrats from 9. The total number of ways to form the committee is 1980.
Step-by-step explanation:
The question is asking how many ways a committee can be formed with 2 Republicans and 2 Democrats, chosen from a pool of 11 Republicans and 9 Democrats. This is a combinatorics problem that can be solved using the combination formula. The combination formula, which is used to determine how many ways k items can be selected from a set of n items, is given by n choose k (nCk) = n! / (k!(n-k)!), where '!' denotes factorial.
First, we'll calculate the number of ways to choose 2 Republicans from the 11 available. This can be calculated using the combination formula:
11C2 = 11! / (2!(11-2)!) = 11! / (2!9!) = (11 × 10) / (2 × 1) = 55.
Next, we calculate the number of ways to choose 2 Democrats from the 9 available:
9C2 = 9! / (2!(9-2)!) = 9! / (2!7!) = (9 × 8) / (2 × 1) = 36.
Since the selections of Republicans and Democrats are independent events, we multiply the two results to find the total number of ways to form the committee:
Total number of ways = 55 × 36 = 1980.
The committee can be formed in 1980 different ways.