Final answer:
There are 36 possible combinations to form a subcommittee with the given number of Republicans, Democrats, and Independents. The calculation involves combinations which are found using the combination formula for each group and multiplying the results together.
Step-by-step explanation:
The problem at hand is a combinatorics problem which involves calculating the number of possible ways to form a subcommittee given a specific number of people from each political affiliation. To find the total number of possible subcommittees, we need to use the combination formula which is C(n, k) = n! / (k!(n-k)!), where 'n' is the total number of options and 'k' is the number of selections made.
For the Republicans, we have C(4, 2) possible selections, for the Democrats C(3, 2) possible selections, and for the Independents C(2, 1) possible selection.
Calculating each we get:
- Republicans: C(4, 2) = 6
- Democrats: C(3, 2) = 3
- Independents: C(2, 1) = 2
To get the total number of possible subcommittees, we multiply these individual combinations together:
Total = Republicans * Democrats * Independents = 6 * 3 * 2 = 36
Therefore, There are 36 possible ways to form the subcommittee. The options for the student are: A) 24 B) 9 C) 36 D) 96. The correct answer is C) 36.