Question

How many teams of 4 can be formed from a class of 30 students?

Answer 1

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.