Question

In a party 100 students shake hands with each and every other student. How many hand shakes will there be ? (

Answer 1

Okay total there were 100 members.

First member will shake hands with 99 people.

Offcourse he will not shake his own hand

Then the next man the 2nd man will come and shake hands with 98 people.

It is because he has already shook his hand with the first person.

So:

the handshakes will go on like this:

99+98+97+96+...................1

This is an AP

with first term a is 99

common difference is -1

number of terms is 99

Sn=(n/2) * [2a + (n-1)*d]

Sn=(99/2) * [ 198 + (98)*(-1) ]

Sn=(99/2) * [198-98]

Sn=(99/2) *  100

Sn=99*50

Sn=4950

There will be 4950 handshakes

Hope it helps.

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Answer 2

Answer:

answer is 4950

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