There are 10 students in a class. A student is allowed to shake hand only once with a student who is taller than him or equal in height to him. He can’t shake hand with anyone who is shorter than him. Average height of the class is 5 feet. What is the difference between the maximum and minimum number of handshakes that can take place in the class?

Answer Choices

Correct answer marked below

Correct

See the full step-by-step explanation

You can see the correct answer above. Sign in for free to unlock the complete worked solution.

Track your performance and improve

Get detailed analytics, unlock full explanations, and move up difficulty tiers as you practice.

Start for free Sign in

Explanation

Preview

Official Explanation

Official

Maximum number of handshakes = when all students are of the same height (they can all shake hands with each other, without any restriction on anybody)

=

_{10}C_{2}

= 45

Minimum number of handshakes = when all students are of different heights (no one can shake hands with anyone, since it's stated that there is a constraint that no taller student can shake hands with a shorter student; if no one is equal in height, for any pair of students we choose, one will be taller/shorter than the other, which prohibits them from shaking hands)…

Read the full explanation

Create free account Sign in

Comments

No comments yet

Be the first to share your thoughts and help others understand it better.

What this question tests

What it tests

Whether you can count arrangements and selections correctly — permutations vs. combinations.

Common trap

Overcounting: treating a selection as ordered when order does not matter, or forgetting to divide by duplicates.