SOLUTION: Ten persons gather for a meeting. Before the meeting begins, each person shakes hands with every other person exactly once. How many handshakes are there altogether?
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Question 1099187: Ten persons gather for a meeting. Before the meeting begins, each person shakes hands with every other person exactly once. How many handshakes are there altogether?
You can put this solution on YOUR website! 10x9/2=45
10 people have to shake hands with 9 other people; but since one handshake takes two people, then A shaking hands with B is the same as B shaking hands with A. So, you take the total number of handshakes and divide by 2 to get the amount of handshakes that actually take place.
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One handshake is a "combination" of two persons.
The term "combination" is used here in its mathematical meaning as it is used in Combinatorics.
Therefore, the total number of handshakes is equal to the total number of combinations of 10 people taken 2 at a time:
= = = 45.
In the general case of n people the formula for the number of handshakes is = .
