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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 correct answer is 21. 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. So the total would be 21...
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.
How many people are there if everyone shakes hands and there are 66 handshakes?
Assuming that each person shakes hands with every other person, there are 12 people. Let n be the number of people. Then each person shakes hands with (n-1) people and if you ask every person how many hand shakes they made and total them you will get a total of n(n-1) handshakes. However, each handshake involves two people and has been counted twice - once by each person that shook hands - thus number of hand shakes is half of this, giving: n(n-1)/2 = 66 ⇒ n(n-1) = 132 ⇒ n2 - n - 132 = 0 ⇒ (n - 12)(n + 11) = 0 ⇒ n = 12 or -11 You can't have -11 people, therefore there are 12 people.
How many hand shakes would take place if 20 people shake hands once?
First person shakes hands 19 times, second person 18 etc, a total of 190.
How many handshakes will be there be in total if 9 people shake hands with each other?
the first shakes 8 people's hands (remember, not his own), the second 7 (he doesn't shake the first one's hand), then the third shakes six, the fourth shakes 5, the fifth shakes 4, the sixth shakes 3, the seventh shakes 2, and the 8th shakes the 9ths hand so 8+7+6+5+4+3+2+1 = 36
If the friends shake hands mutually then the total number of hand shakes is?
one....
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
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.
In a party of 35 people shake hand with everyone?
595 If you have 35 people and everyone shakes hands with everone else, you have 35x34/2 total handshakes. To see this think of three people, and fix one of them, say it's you! You shake hands with everyone meaning you shake hands with 2 people And each of them shakes hands with each other, that is two people other than you so the total 2+1= 3 which is 3x2/2 Try it with 4, you shake hand with 3 people, and they all shake hands with each other so we have your 3 plus 3 more. To see the three more, just look at what we just did above. 4x3/2=6, We divide by 2 to avoid double counting. Because you shake hands with me and I shake hands with you, but we only shake hands once, so divide the total by 2. In general for n people at a party, we have n(n-1)/2handshakes.
When ten people in a room shake hands with everyone else how many handshakes will there be in total?
Person A shakes with nine people (B through J).Person B shakes with eight (C through J because he's already shaken hands with A). Person C shakes with seven, D with six, all the way down to person J, who has already shaken with everyone else. So, 9+8+7+6+5+4+3+2+1+0=45 shakes.
In a party everyone shakes hand with each other. If total number of handshakes is 780 how many people were there?
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.
Everybody in a party shakes hands with everybody else the total number of persons in the room are 12How many ways are there of shaking hands?
66 total handshakes are made. See related question at the bottom for the explanation.
