36. Everybody shakes 8 hands but each shake counts for 2 people. So 9*8/2=36.
20 hand shakes would take place. Here's how: 1234567 23456 34567 4567 567 67 7 And a person can't shake his own hand or someones hands twice
45 handshakes
4950
210
25 shakes
36. Everybody shakes 8 hands but each shake counts for 2 people. So 9*8/2=36.
First person shakes hands 19 times, second person 18 etc, a total of 190.
1 999 000
20 hand shakes would take place. Here's how: 1234567 23456 34567 4567 567 67 7 And a person can't shake his own hand or someones hands twice
45 handshakes
4950
210
72
105 ( First person shakes 14 different hands, second shakes 13 etc etc down to 14th shakes 1 hand. Sum of 1 to 14 = 105.)
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
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.