<p>Model Test #1, #38</p>
<p>28 handshakes occur in a room where each person shakes another person's hand one time. How many people are in the room?</p>
<p>This is a combination type problem right?</p>
<p>Let x=number of people</p>
<p>You do XCr2=28</p>
<p>That means X!/(2!)((X-2)!)=28</p>
<p>This is reduced to</p>
<p>X!/2(X-2)!=28</p>
<p>X!/(X-2)!=56</p>
<p>You have to think a little bit about how to simplify for this next part:</p>
<p>X(X-1)=56
x^2-X-56=0
(x-8)(X+7)=0</p>
<p>x=8</p>