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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
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If There are 5 people at a party Each person must shake hands once with every other person at the party How many handshakes does it take to do this?
10 times
Seven people shake hands once how many times do they shake hands?
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.
How many hand shakes if 12 people shake hands with every other person in room?
72
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.
What is the angle of the hands of a clock at 7.10?
The two hands make an angle of 155 degrees (and 205 degrees).
