Final answer:
The total number of ways a delegation of 5 Republicans, 5 Democrats, and 1 Independent can be elected from a group of 6 Republicans, 6 Democrats, and 2 Independents is 72.
Step-by-step explanation:
To find the number of ways a delegation can be elected, we need to use the concept of combinations. We have 6 Republicans, 6 Democrats, and 2 Independents, and we need to select 5 Republicans, 5 Democrats, and 1 Independent.
The number of ways to select 5 Republicans from 6 is denoted as C(6, 5) = 6.
The number of ways to select 5 Democrats from 6 is denoted as C(6, 5) = 6.
The number of ways to select 1 Independent from 2 is denoted as C(2, 1) = 2.
By using the Multiplication Principle, we can multiply the number of ways for each group together:
Total number of ways = C(6, 5) * C(6, 5) * C(2, 1) = 6 * 6 * 2 = 72.
Therefore, there are 72 ways a delegation of 5 Republicans, 5 Democrats, and 1 Independent can be elected from the given group.