Three people (1 couple and 1 single) are seated at random in a row of 7 chairs. What is the probability that the couple does not sit together? Pick
A) 3/7  B) 4/7  C) 5/7  D) 6/7  E) 9/14
The total number of arrangements of 3 people is   7*6*5= 
<gadget id="calculator">  7*6*5</gadget>
<output>210</output>
210   Let's think of the couple as a single unit.   The number of arrangements when the couple sits together is 6*5*2= 
<gadget id="calculator">6*5*2</gadget>
<output>60</output>
60.   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  210 - 60= 
<gadget id="calculator"> 210 - 60</gadget>
<output>150</output>
150   P(couple won't sit together)= 150/210 = 5/7   The answer is 5/7.
<result>C</result>
Three people (1 couple and 1 single) are seated at random in a row of 7 chairs. What is the probability that the couple does not sit together?