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Q: Five people shake hands with every one how many shakes were there?

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72

36. Everybody shakes 8 hands but each shake counts for 2 people. So 9*8/2=36.

45 handshakes

4950

210

105 ( First person shakes 14 different hands, second shakes 13 etc etc down to 14th shakes 1 hand. Sum of 1 to 14 = 105.)

Perhaps 9,900 As in you shake with 99 other people, then the next person does the same. So each of the 100 people do 99 shakes. 99 x 100 = 9,900

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

First person shakes hands 19 times, second person 18 etc, a total of 190.

one....

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.

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.

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