I think the answer is 45
1|2,3,4,5,6,7,8,9,10
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2|3,4,5,6,7,8,9,10
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3|4,5,6,7,8,9,10
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4|5,6,7,8,9,10
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5|6,7,8,9,10
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6|7,8,9,10
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7|8,9,10
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8|9,10
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9|10
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10|he already shake hand with everybody
Solving with the claculator(TI-36X Solar)
1.Enter the total of people(10)
2.Hit the button that looks like this x<->y
3.Enter 2 (when shaking hands need two persons)
4.Hit third function, nCr