Question 186612
<pre><font size = 4  color = "indigo"><b>
"5 choose 2":

{{{5C2 = 5!/(2!(5-2)!)=5!/(2!3!)=(5*4*3*2*1)/((2*1)(3*2*1))}}}

Canxcel the two 2's into the 4

{{{(5*cross(4)*3*2*1)/((cross(2)*1)(3*cross(2)*1))}}} 

Cancel the 3's

{{{(5*cross(4)*cross(3)*2*1)/((cross(2)*1)(cross(3)*cross(2)*1))}}}

You are left with {{{5*2}}} or {{{10}}} ahndshakings.

If the people are A,B,C,D, and E, they are
 
 1. A shakes hands with B
 2. A shakes hands with C
 3. A shakes hands with D
 4. A shakes hands with E
 5. B shakes hands with C
 6. B shakes hands with D
 7. B shakes hands with E
 8. C shakes hands with D
 9. C shakes hands with E
10. D shakes hands with E

Edwin</pre>