document.write( "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? \n" ); document.write( "

Algebra.Com's Answer #699873 by natolino_2017(77) $\"\"$ $\"About$

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