72
For everyone to shake hands with everyone else, there are 21 handshakes. (below copied from my answer of a similar question) This is an arithmetic progression and can be solved with the equation Sn=(1+(n-1))(n-1)/2 where Sn is the total sum of handshakes for n people. NB: I have used n-1 instead of n in the equation for the sum of an arithmetic progression, because you're not really going to shake hands with yourself, so you don't include the nth term, in this case 7. Alternatively, you can solve this geometrically by drawing a heptagon, drawing lines between all the vertices, and then adding all the lines up.
10 times
A "square" of shakes covers 100 SF of wall or roof area. Beyond that - everything depends on the installation. The number of actual pieces of wood in a square varies greatly based on the exposure the installer wants to leave, and the width of the shakes, which are normally bundled random in width. A single handsplit shake is going to be 18" in length and be installed with an exposure anywhere from 4"-7" . It could be anywhere from 3-12" in width. It typically takes 4-6 bundles of shakes to get 100SF of exposure, but again that varies wildly based on the product and how it is installed. Note that cedar "Shakes" are typically hand-split and will vary greatly- whereas cedar "shingles" are machine cut and can be ordered in uniform width if desired.
The first person can be selected in one of seven ways. Having selected him, the second can be selected from the remaining six in six ways. So there would appear to be 7*6 ways of selecting the couples shaking hands. But, x shaking y's hand is the same handshake as y shaking x's hand. Thus each handshake is conted twice, So the total number of handshakes is 7*6/2 = 21
25 shakes
36. Everybody shakes 8 hands but each shake counts for 2 people. So 9*8/2=36.
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
If each person is shaking with only one hand, then the answer is seven. If they are shaking with both hands, then the answer is 14.
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.