Final answer:
To find the number of handshakes that take place when four people shake hands with one another exactly once, you can use the concept of combinations. Using the formula for combinations, 4C2 = 6 handshakes.
Step-by-step explanation:
To find the number of handshakes that take place, we need to use the concept of combinations. When four people shake hands with one another exactly once, we are essentially choosing two people at a time to shake hands. Using the formula for combinations, which is nCr = n! / (r!(n-r)!), where n is the total number of people and r is the number of people chosen at a time, we can calculate the number of handshakes.
In this case, n = 4 and r = 2. Plugging these values into the formula, we get 4C2 = 4! / (2!(4-2)!) = 4! / (2!2!) = (4x3x2x1) / (2x1x2x1) = 24 / 4 = 6.
So, there are 6 handshakes that take place when four people shake hands with one another exactly once.