Final answer:
There can be 27,405 different teams of 4 formed from a class of 30 students, calculated using combinations.
Step-by-step explanation:
To determine how many teams of 4 can be formed from a class of 30 students, we use the combination formula which is given by:
C(n, k) = n! / (k! * (n - k)!).
Where:
- n is the total number of items,
- k is the number of items to choose,
- ! (exclamation point) denotes factorial, the product of all positive integers up to that number.
For this question:
- n = 30 (the total number of students),
- k = 4 (the number of students for each team).
The calculation is as follows:
C(30, 4) = 30! / (4! * (30 - 4)!).
This simplifies to:
C(30, 4) = 30! / (4! * 26!).
After canceling out the common terms (26!), we're left with:
C(30, 4) = (30 * 29 * 28 * 27) / (4 * 3 * 2 * 1).
Performing the multiplication and division, we get:
C(30, 4) = 27,405.
Therefore, 27,405 different teams of 4 can be formed from a class of 30 students.