Calculating Handshakes Among Doctors
The Scenario
In a conference room, there are five doctors present. Each doctor engages in a handshake with every other doctor precisely one time.
Determining Total Handshakes
To find the total number of handshakes that occur, we can use the formula for combinations. Specifically, we need to calculate how many ways we can choose 2 doctors from a group of 5 to shake hands.
The Solution
Using the combination formula, we have:
C(n, k) = n! / (k!(n – k)!)
For our situation, n = 5 (the total number of doctors) and k = 2 (the number of doctors shaking hands at one time).
C(5, 2) = 5! / (2!(5 – 2)!) = (5 × 4) / (2 × 1) = 10.
Therefore, the total number of handshakes that occur is 10.