Table of Contents

- 1 What is the formula for the handshake problem?
- 2 How many handshakes will there be if six guests shake hands with all the others once?
- 3 How many handshakes are in a party?
- 4 How many handshakes possible if there are 8 people in a room and each one shakes hands of the others once?
- 5 How many handshakes occurred at a party?
- 6 How many handshakes are there in 20 19?

## What is the formula for the handshake problem?

# handshakes = n*(n – 1)/2. This is because each of the n people can shake hands with n – 1 people (they would not shake their own hand), and the handshake between two people is not counted twice. This formula can be used for any number of people. # handshakes = 10*(10 – 1)/2.

**How many hand shakes would happen in a room with 20 people?**

You know that the total number of persons is 20 , so every person shakes hands with 19 persons.. It then mean that, there are 20×19=380 handshakes. But by every handshake two persons are involved. Therefore, 380 is the result of double-counting, which gives 190 handshakes.

**When 10 persons shake hands with one another in how many ways is it possible?**

Detailed Solution ∴ The total possible number of ways = 45.

### How many handshakes will there be if six guests shake hands with all the others once?

5 handshakes

If a sixth person comes and shakes hands with the other five people that makes a total of 10 + 5 = 15 handshakes. Another way of looking at the problem is that each person has to shake hands with all the others. If there are 6 people each person has 5 handshakes to make.

**How many shake hands are possible?**

190 is the answer. Every person shakes hands with 19 persons, so at first sight there are 20×19=380 handshakes. But by every handshake two persons are involved. So 380 is the result of double-counting.

**How many handshakes can be made in a room of 7 people?**

The Number of Handshakes Required for Different Sized Groups

Number of People in the Room | Number of Handshakes Required |
---|---|

5 | 10 |

6 | 15 |

7 | 21 |

8 | 28 |

#### How many handshakes are in a party?

**What is the minimum amount of handshakes that can occur among fifteen people in a meeting if each person only shakes each other person’s hand once?**

Correct answer: This is a combination problem of the form “15 choose 2” because the sets of handshakes do not matter in order. (That is, “A shakes B’s hand” is the same as “B shakes A’s hand.”) Using the standard formula we get: 15!/((15 – 2)!

**How many total handshakes were there?**

## How many handshakes possible if there are 8 people in a room and each one shakes hands of the others once?

56 handshakes occur in ths event.

**How many handshakes are there altogether?**

Thus in all cases the number of hand shakes is (n−1)+(n−2)+⋯+1=n(n−1)/2. Count person by person, ignoring handshakes with people already counted, to see this. 190 is the answer. Every person shakes hands with 19 persons, so at first sight there are 20×19=380 handshakes.

**How many handshakes if there are 100 people?**

4950 handshakes

What if there were 100 people in the room? = 49(100) + 50 = 4950 handshakes.

### How many handshakes occurred at a party?

At a party 66 handshakes occurred. Each person shook hands exactly once with each of the other people present. How many people were present? | Socratic At a party 66 handshakes occurred. Each person shook hands exactly once with each of the other people present.

**How many times did each person shake hands with each person?**

Each person shook hands exactly once with each of the other people present. How many people were present? Let’s start with small numbers of people and handshakes and move from there. I’ll represent people with letters to show the handshakes:

**What is the formula to calculate the number of handshakes?**

# handshakes = n*(n – 1)/2. This is because each of the n people can shake hands with n – 1 people (they would not shake their own hand), and the handshake between two people is not counted twice. This formula can be used for any number of people. For example, with a party of 10 people, find the number of handshakes possible.

#### How many handshakes are there in 20 19?

It then mean that, there are 20 × 19 = 380 handshakes. But by every handshake two persons are involved.