We don't shake hands with enemies.

Probability Level 3

3016 people are sitting on a circular table. One person shakes hand with everyone except the 100 people who sit beside him (50 on left & 50 on right). Find the total number of handshakes.


The answer is 4395820.

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Rajdeep Dhingra by Rajdeep Dhingra , 20, India

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1 solution

Archit Boobna
Apr 18, 2015

There are 3016 people.

Every person is shaking hands with every person except 101 people (himself and 100 others). So no. of people is 3016-101=2915

Each handshake involves two people, so answer is 3016X2915/2= 4395820 \boxed{4395820}

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I don't understand why you divide by two. The first person makes 2915 handshakes, then the second person makes 2915 handshakes, then the third person makes 2915 handshakes, and so on. So the total number of handshakes should be 3016*2915. What did I do wrong?

Austin Cheng - 6 years, 1 month ago

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Suppose in the very first hand shake A has to shake hands with B. Now When A's term is completed we'll move to count hand shakes done by B.In this case we will again be counting the handshake of B with A.So the handshake that takes place between A n B is being counted twice. This will happen to every two person sitting on a circular table. So we have to divide the final answer by 2. So that No of exact handshakes can be calculated. Tell me if you've got it.

Rahul Gupta - 6 years, 1 month ago

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