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In a party everyone shakes hand with each other. If total number of handshakes is 780 how many people were there?
Wiki User
∙ 9y ago
There were 40 people at the party.
Let n be the number of people at the party.
Each person shakes hands with every other person, so each person shakes hands with (n - 1) people, a possible total of n(n - 1) handshakes.
But when person A shakes hands with person B, B also shakes hands with A, so each handshake would be counted twice.
→ number_of_handshakes = n(n - 1)/2
total number of handshakes is 780
→ n(n - 1)/2 = 780
→ n(n - 1) = 1560
→ n^2 - n - 1560 = 0
As 1560 is negative, one factor is positive and one is negative, so we need the factor pair of 1560 which has a difference of 1, namely: 39 x 40
→ (n - 40)(n + 39) = 0
→ n = 40 or -39
There cannot be a negative number of people → there are 40 people present.
Wiki User
∙ 9y ago
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∙ 14y ago12
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How many people are at a party with 741 handshakes if everyone shakes once?
371
How many handshakes can occur between 5 people if everyone shakes hands?
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In a room there are N number of people if everyone shakes hands how many handshakes are made?
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If at a party there are a total of 741 handshakes and each person shakes hands with everyone else at the party exactly once how many people are at the party?
38
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.
Four people in a room. Each shakes hands with each of the others once. How many handshakes are there?
9 handshakes correct answer is 10
If there are 8 people at a party and every person shakes hands with everyone else at the party how many handshakes will there be?
There will be 28 handshakes. If you ask each person how many handshakes they had they will tell you 7 making 7 x 8 = 56 handshakes in all. But every hand involves two people, so every handshake has been counted twice, thus there are 56 / 2 = 28 handshakes in all.
How many shakes if there are four people?
4*3/2 = 6 handshakes.
Seven people come to a party and shakes hands with each other if each person shakes the hand of every other person how many hand shakes occur?
If there are seven people, then the number of handshakes is 7*6/2 = 21
If ten people are at a party and they all exchange handshakes how many hand shakes were exchanged?
If that happens you have to times ninexten and the answer would be 90 handshakes
