SOLUTION: At a dinner you count 5 people. If everybody wants to clink glasses with everybody, how many times do they clink the glasses in total?

Question 1085786: At a dinner you count 5 people. If everybody wants to clink glasses with everybody, how many times do they clink the glasses in total?
Answer by natolino_2017(77) (Show Source): You can put this solution on YOUR website!
Every person clinks their glasses, acoording to the rule the first person make n-1, the second person has already make the toast with the first person, so he clinks (n-2) times and so, it goes on until the (n-1) person make only one toast.

So total clinks are = (n-1) + (n-2) + (n-3)+... + 1.
So using the formula for an arithmetic progession.
Total Clinks = (n-1+1)(n-1)/2 =(n^2-n)/2.
in this case n=5, so answer is = (5^2-5)/2 = 10.
@natolino_
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