Three people (1 couple and 1 single) are seated at random in a row of 4 chairs. What is the probability that the couple does not sit together?  Select:
A) 3/7  B) 1/2  C) 2/5  D) 3/4  E) 5/12
The total number of arrangements of 3 people is   4*3*2= 
<gadget id="calculator">  4*3*2</gadget>
<output>24</output>
24   Let's think of the couple as a single unit.   The number of arrangements when the couple sits together is 3*2*2= 
<gadget id="calculator">3*2*2</gadget>
<output>12</output>
12.   Note that we multiply by 2 because the couple can switch places with each other.   The number of ways the couple won't sit together is  24 - 12= 
<gadget id="calculator"> 24 - 12</gadget>
<output>12</output>
12   P(couple won't sit together)= 12/24 = 1/2   The answer is 1/2.
<result>B</result>
Three people (1 couple and 1 single) are seated at random in a row of 4 chairs. What is the probability that the couple does not sit together?