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?

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?

Found 2 solutions by jorel1380, ikleyn:
Answer by jorel1380(3719)   (Show Source): 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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Answer by ikleyn(52790)   (Show Source): You can put this solution on YOUR website!
.

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 = .

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On Combinations, see the lessons
    - Introduction to Combinations
    - PROOF of the formula on the number of Combinations
    - Problems on Combinations
    - OVERVIEW of lessons on Permutations and Combinations
in this site.

Also, you have this free of charge online textbook in ALGEBRA-II in this site
    - ALGEBRA-II - YOUR ONLINE TEXTBOOK.

The referred lessons are the part of this online textbook under the topic "Combinatorics: Combinations and permutations".

Save the link to this textbook together with its description

Free of charge online textbook in ALGEBRA-II
https://www.algebra.com/algebra/homework/complex/ALGEBRA-II-YOUR-ONLINE-TEXTBOOK.lesson

into your archive and use when it is needed.

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