# C++ Program to find the maximum number of handshakes

## Maximum Number of Handshakes in C++

Here we will discuss how to find the maximum number of handshakes which can happen between N number of people given the fact that any two people shake hands exactly once using C++ programming language.

### Approach :

For the number of handshakes to be maximum, every person should hand-shake with every other person in the room

i.e. all persons present should shake hands.

• For the first person, there will be N-1 people to shake hands with
• For second person, there will be N -1 people available but as he has already shaken hands with the first person, there will be N-1-1 = N-2 shake-hands
• For third person, there will be N-1-1-1 = N-3, and So On…

Therefore the total number of handshake   =   ( N – 1 + N – 2 +….+ 1 + 0 )   =   ( (N-1) * N ) / 2.

### Algorithm

• For N = 8
• handshakes  =  ( (N-1) * N ) / 2  =  ( 8 x 7 )/2  =  28
• Print Result

### C++ Code

Run
```// C++ program to find the maximum number of handshakesM
#include<iostream>
using namespace std;

int main()
{

//fill the code
int num = 9;

int total = num * (num-1) / 2; // Combination nC2

cout<<"For "<<num<<" people there will "<<total<<" handshakes";

return 0;

}```

### Output

`For 8 people there will be 28 handshakes`