There are 40 students in a class. A student is allowed to shake hands only once with a student who is taller than him or equal in height to him. He cannot shake hands with somebody who is shorter than him. The average height of the class is 5 feet. What is the difference between the maximum and the minimum number of handshakes that can happen in such a class?
If all are of equal height, the number of handshakes = `"^40C_2`
If all are of different heights, the number of handshakes = 0
∴ Required Difference = `"^40C_2-0=^40C_2`