Final answer:
The problem is a combinatorics question where the principal can choose 125,970 different committees of 8 students from a 20-member student council using the combination formula.
Step-by-step explanation:
This question is a classic example of a combination problem in mathematics, specifically combinatorics. To determine how many different committees can be chosen, we use the combination formula:
C(n, k) = n! / (k!(n-k)!)
where n is the total number of items to choose from, k is the number of items to choose, and ! denotes factorial.
In this case, there are 20 members in the student council and the principal wants to choose 8, so we plug those numbers into the formula:
C(20, 8) = 20! / (8!(20-8)!) = 20! / (8!12!) = 125,970
Therefore, there are 125,970 different ways the committee of 8 students can be chosen from the 20-member student council.