Word Problem

Probability Level 1

At a party, everyone shook hands with everybody else. In total, there were 66 handshakes. How many people were at the party?

10 14 11 12 18

Natey T by Natey T , 19, USA

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2 solutions

Ivan Umezu
Feb 4, 2016

As it is a combination between 2 people out of n people, we have: C n,2 = n!/(n-2)! × 2! = 66 Simplifying, n^2 - n - 132 = 0 Solving the equation, we have 12 as the answer.

3 Helpful 0 Interesting 0 Brilliant 0 Confused
Natey T
Feb 4, 2016

If everyone shook handshakes, there were then we can use the Gauss formula of n(n+1)/2. In this case we write:

n(n+1)/2 = 66

When solving it we get the quadratic equation n^2+ n -132 = 0. Solving for n, we obtain 11 as the answer. BUT, WE ARE NOT DONE YET... we then remember that it must be n+1, so 11+1 = 12. We get 12 as the answer.

2 Helpful 0 Interesting 0 Brilliant 0 Confused

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