How many different 3-person committees can be selected from a group of 8 people?

Step 1: Decide whether order matters.

We are selecting a committee of 3 people.

The order in which the people are selected does not matter. For example, choosing Ana, Ben, and Chris produces the same committee as choosing Chris, Ana, and Ben.

Therefore, we use combinations rather than permutations.

Step 2: Recall the combination formula.

C(n, r) = n! / (r!(n - r)!)

Here:
n = 8
r = 3

Step 3: Substitute the values.

C(8, 3) = 8! / (3!5!)

Step 4: Cancel the common factorial terms.

8! / (3!5!) = (8 × 7 × 6) / (3 × 2 × 1)

Step 5: Calculate.

8 × 7 × 6 = 336
3 × 2 × 1 = 6

336 / 6 = 56

Therefore, 56 different 3-person committees can be selected.