Three people (1 couple and 1 single) are seated at random in a row of 8 chairs. What is the probability that the couple does not sit together? Select the correct option:
A) 2/3  B) 2/5  C) 3/8  D) 3/4  E) 4/5
The total number of arrangements of 3 people is   8*7*6= 
<gadget id="calculator">  8*7*6</gadget>
<output>336</output>
336   Let's think of the couple as a single unit.   The number of arrangements when the couple sits together is 7*6*2= 
<gadget id="calculator">7*6*2</gadget>
<output>84</output>
84.   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  336 - 84= 
<gadget id="calculator"> 336 - 84</gadget>
<output>252</output>
252   P(couple won't sit together)= 252/336 = 3/4   The answer is 3/4.
<result>D</result>
Three people (1 couple and 1 single) are seated at random in a row of 8 chairs. What is the probability that the couple does not sit together?