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 - Mathematics

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MCQ

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?

Options

  • `(("^40C_2)/2-20)`

  • 361

  • `"^40C_2-40`

  • `"^40C_2`

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Solution

`"^40C_2`
Explanation:
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`

Concept: Permutation and Combination (Entrance Exam)
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