Hand shakes

Probability Level 1

10 members of the residence welfare committee met for their monthly meeting. Each one shakes hands with every other person in the room once. Find the total number of handshakes.

56 handshakes 81 handshakes 100 handshakes 45 handshakes

Adhiraj Chopra by Adhiraj Chopra , 22, India

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5 solutions

Sravanth C.
Jun 30, 2015

We know that the first person will give 9 9 handshakes(because he can't be included!)

The second person - 8 8 , the third person - 7 7 , the fourth - 6 6 and so on . . .

So, the total no. of handshakes = 9 + 8 + 7........ + 1 = = 9+8+7 . . . . . . . .+1 = 9 × 10 2 = \displaystyle\frac{9\times10}{2}= 45 \boxed{45}

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Moderator note:

There is no need to write the first line. And your solution is wrong. How does 10 × 11 2 = 45 \frac{10\times11}2 = 45 ?

Lucas Nascimento
Oct 21, 2015

Another useful way to do is consider a polygon of 10 vertexes and to sum its diagonals with its sides. 35 diagonals + 10 sides = 45 lines Each line that unites two vertexes represents a different handshake.

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Deepak Tomar
Jul 4, 2015

Out of 10 persons... pick any two persons and make them shake hand ... so solution becomes choosing 2 out of 10 = 10C2=45.

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Department 8
Jun 30, 2015

You can use combinations for this.

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Praful Jain
Jun 30, 2015

First person shakes hand with 9 people, second with 8 ,third with 7 so no of handshakes are 9 + 8 + 7 + 6......+1= 45 handshakes

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