Three people (1 couple and 1 single) are seated at random in a row of 6 chairs. What is the probability that the couple does not sit together?  Answers.
A) 2/3  B) 4/5  C) 2/7  D) 3/5  E) 5/12
The total number of arrangements of 3 people is   6*5*4= 
<gadget id="calculator">  6*5*4</gadget>
<output>120</output>
120   Let's think of the couple as a single unit.   The number of arrangements when the couple sits together is 5*4*2= 
<gadget id="calculator">5*4*2</gadget>
<output>40</output>
40.   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  120 - 40= 
<gadget id="calculator"> 120 - 40</gadget>
<output>80</output>
80   P(couple won't sit together)= 80/120 = 2/3   The answer is 2/3.
<result>A</result>
Three people (1 couple and 1 single) are seated at random in a row of 6 chairs. What is the probability that the couple does not sit together?