In how many ways can a committee of 4 be chosen from a group of 8 people?

To determine how many ways we can choose a committee of 4 from a group of 8 people, we can use the concept of combinations. Combinations are used when the order of selection does not matter.

The formula for combinations is given by:

C(n, k) = n! / (k! * (n – k)!)

Where:

• n is the total number of items (in this case, 8 people).
• k is the number of items to choose (in this case, 4 people).

In our scenario:

n = 8 and k = 4

Plugging in the values, we have:

C(8, 4) = 8! / (4! * (8 – 4)!)

This simplifies to:

C(8, 4) = 8! / (4! * 4!)

Calculating this step-by-step:

1. 8! = 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1
2. 4! = 4 × 3 × 2 × 1 = 24

Now we can simplify:

C(8, 4) = (8 × 7 × 6 × 5) / (4 × 3 × 2 × 1)

Calculating the numerator:

8 × 7 = 56
56 × 6 = 336
336 × 5 = 1680

And for the denominator:

4 × 3 = 12
12 × 2 = 24

Putting it all together:

C(8, 4) = 1680 / 24 = 70

So, there are 70 different ways to form a committee of 4 people from a group of 8.