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14 is incorrect

Correct answer is 21*

7 persons in total, which means the first one will shake hands with 6 persons, the next in line will shake hands with 5 (given that he already shook hands with the first person).

Calculation is: 6+5+4+3+2+1=21

*Applies to question if handshakes take place between new partners only, however in either case 14 can never be the answer.

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Elmira Buhayova

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6mo ago
Incorrect
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我們一家都很蔡(Alston)

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3mo ago
21
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Contessa Nunez

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3y ago

Problem 5

If seven people meet each other and each shakes hands only once with each of the others, how many handshakes will there have been?

The first person will shake hands with the other 6 people. The second person, having already shaken hands with the first person, will shake 5 more hands, making a total thus far of 11. The next person in similar fashion will shake 4 more hands. If we continue in this manner, we end up with

6 + 5 + 4 + 3 + 2 + 1 + 0 = 21

This is something in math that we call the‘Handshake Lemma’. If

there are n people, the number of handshakes will always be

n(n+1) 2

This is a common formula when working with counting problems.

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Q: There are 7 people at a party Each person must shake hands with all the other people at the party once How many handshakes does it take to do this?
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How many handshakes if 25 people shake hands with every other person in room?

Each person will shake hands with every other person, except himself. If there are 25 people, each person will shake hands with 25-1 people, or 24. The number of times each person will shake hands with another, will be 25x24. The number of handshakes will be half of that, as each handshake is between two persons. The formula, in other words, is x(x-1)/2, where x is the number of people. With 25 people, it will be 25x24/2 = 300 handshakes.


If at a party there are twelve people present Everyone has to shake hands exactly once with every other person How many handshakes are necessary?

Sixty-six unique, distinct handshakes.


There are 6 people at a party If each person must shake hands with every other person at the party exactly once, how many handshakes will there be?

The first person must shake hands with 5 other people. The next must shake hands with 4 other people, since you exclude the first person. Keep going and you'll find that there will be 5+4+3+2+1=15 handshakes. Numbers like this are called triangular numbers.


There are 6 people at a party If each person must shake hands with every other person at the party exactly once how many handshakes will there be?

15


At the end of a banquet 5 people shake hands with each other How many handshakes will there be in total?

Each person shakes hands with every other person at the end of the banquet. When person 1 shakes hands with person 2 that constitutes one handshake even though 2 people are involved. So the answer is 10 total handshakes because the 1st person will have 4 total handshakes(because he can't shake hands with himself, he has 4 and not 5 total handshakes), and then the 2nd person will have 3 total handshakes (you wouldn't say 4 handshakes because you've already included the handshake between person 1 & person 2 when calculating the first person's number of shakes) and so on for the remaining 3 people. On paper the math would look like this: 4+3+2+1=10 Alternatively: Each person shakes hands with 4 others so the answer looks like 5x4 = 20; However, in Fred shaking with 4 others, he shakes with Charlie, similarly, in Charlie shaking with 4 others he shakes with Fred. Thus the Fred-Charlie handshake has been counted twice (once by Fred, once by Charlie), as have all the handshakes, thus the answer is: 5x4 / 2 = 10.

Related questions

How many handshakes if 20 people shake hands with every other person in the room?

190


How many handshakes if 25 people shake hands with every other person in room?

Each person will shake hands with every other person, except himself. If there are 25 people, each person will shake hands with 25-1 people, or 24. The number of times each person will shake hands with another, will be 25x24. The number of handshakes will be half of that, as each handshake is between two persons. The formula, in other words, is x(x-1)/2, where x is the number of people. With 25 people, it will be 25x24/2 = 300 handshakes.


There are five people in a room Each person shakes the hand of every other person exactly once How many handshakes are exchanged?

Everyone shakes hands with 4 other people. Since there are 5 people in the room this would suggest there are 5*4 = 20 handshakes. However, you would then be double counting handshakes: A shaking hands with B and B shaking hands with A is, in reality, only one handshake. Thus there are 5*4/2 = 10 handshakes in all.


How many handshakes if 4 people shakes hands with every other person in the room?

Type your answer here... 6


If at a party there are twelve people present Everyone has to shake hands exactly once with every other person How many handshakes are necessary?

Sixty-six unique, distinct handshakes.


If each of seven persons in a group shakes hands with each of the other six persons then a total of forty-two handshakes occurs?

The answer is 21 handshakes because the first person shakes hands with the other 6 people. The second person shakes hands with 5 people because they already shook hands with the first person. The third person shakes hands with 4 people because they already shook hands with the first and second person. The fourth person shakes hands with 3 people because they already shook hands with the first, second, and third. The fifth person shakes hands with 2 people because they already shook hands with the first, second, third, and fourth person. The sixth person shakes hands with the seventh person because the rest have already shaken hands with them. The seventh person doesn't have anyone else to shake hands with. Therefore the answer is 21 handshakes.


There are 6 people at a party If each person must shake hands with every other person at the party exactly once, how many handshakes will there be?

The first person must shake hands with 5 other people. The next must shake hands with 4 other people, since you exclude the first person. Keep going and you'll find that there will be 5+4+3+2+1=15 handshakes. Numbers like this are called triangular numbers.


There are 3 people at a party If each person must shake hands with every other person at the party exactly once how many handshakes will there be?

With 3 people, there are only 3 handshakes: AB, AC, and BC. Where it gets interesting is at a party with, say, 10 people ... 45 handshakes. Or in the US Senate when all 100 Senators are present ... 4,950 handshakes.


There are 6 people at a party If each person must shake hands with every other person at the party exactly once how many handshakes will there be?

15


How many handshakes if 6 people shakes hands with every other person in the room?

If there are 6 people in a room, and each person shakes hands with every otherperson in the room, then there will be 15 separate and distinct handshakesbetween different pairs of people.


If There are 5 people at a party Each person must shake hands once with every other person at the party How many handshakes does it take to do this?

10 times


How many handshakes will there be altogether at the end of a business conference if the ten people present all shake hands with each other once?

There will be 45 handshakes (assuming that each person doesn't repeat who they shake hands with). Use the following formula for this one (n*(n-1))/2 where n is number of people...so if 10 people its (10 x 9) / 2 = 45 handshakes, if 7 people its (7 x 6) / 2 = 21 handshakes etc.