To determine the number of ways to choose a committee of 4 members from a group of 8 people, we can use the concept of combinations. Combinations are used when the order of selection does not matter. This can be expressed mathematically using the binomial coefficient, often denoted as C(n, k), where n is the total number of items to choose from and k is the number of items to choose.
In this case, we have:
n = 8(the total number of people)k = 4(the number of people to choose for the committee)
The formula for combinations is given by:
C(n, k) = n! / (k! * (n - k)!)
Plugging in our values:
C(8, 4) = 8! / (4! * (8 - 4)!)
C(8, 4) = 8! / (4! * 4!)
Now, let’s calculate the factorials:
8! = 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1 = 403204! = 4 × 3 × 2 × 1 = 24
Substituting these values back into our combination formula:
C(8, 4) = 40320 / (24 * 24)
C(8, 4) = 40320 / 576 = 70
Thus, there are 70 different ways to form a committee of 4 members from a group of 8 people.