QuestionHow many handshakes occur when 4 people each shake hands once? Generalize for $n$ people. Simplify your answer.

Studdy Solution
Calculate the number of handshakes.
$$C(4,2) = \frac{24}{4} =6$$So, for four people, there will be6 handshakes.
b. For $n$ people, the number of handshakes can be generalized as followsThe number of handshakes for $n$ people is the number of ways to choose2 people out of $n$. So, we can use the combination formula again.
$$C(n,2) = \frac{n!}{2!(n-2)!}$$This is the generalized solution for $n$ people.