Assuming a group of 8 people, find out how many different ways there are to select a committee of 3.
user
Sure, I'd be happy to help you with that. This is a classic problem in combinatorics, also known as "Committee Problem."

The number of ways to select a committee of 3 from a group of 8 people is given by the binomial coefficient, which is denoted by the symbols "C" (for "combination") or "!" (for "factorial"), followed by the number of items (8) and the number of to-be-selected items (3), separated by a line (C(8,3) = 8!/3!5! = 56).

In this case, the number of ways to select a committee of 3 is 56, so there are 56 different committees that can be formed from a group of 8 people.

I hope this helps! Let me know if you have any further questions.
assistant
Assuming a group of 8 people, find out how many different ways there are to select a committee of 3.
user
To find the number of different ways to select a committee of 3 from a group of 8 people, we will use the combination formula. The combination formula is used when the order does not matter and is given by:

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

where C(n, k) represents the number of combinations of choosing k items from a set of n items, n! denotes the factorial of n, and k! denotes the factorial of k.

In this case, n = 8 (total number of people), and k = 3 (number of people to be selected for the committee).

C(8, 3) = 8! / (3!(8-3)!)
          = 8! / (3!5!)
          = (8 × 7 × 6 × 5 × 4 × 3 × 2 × 1) / ((3 × 2 × 1)(5 × 4 × 3 × 2 × 1))
          = (8 × 7 × 6) / (3 × 2 × 1)
          = 56 / 6
          = 56 ÷ 6
          = 28

So, there are 28 different ways to select a committee of 3 people from a group of 8.
assistant