Three people (1 couple and 1 single) are seated at random in a row of 9 chairs. What is the probability that the couple does not sit together?	Options
A) 3/4
B) 4/7
C) 5/8
D) 5/9
E) 7/9
The total number of arrangements of 3 people is   9*8*7= 
<gadget id="calculator">  9*8*7</gadget>
<output>504</output>
504   Let's think of the couple as a single unit.   The number of arrangements when the couple sits together is 8*7*2= 
<gadget id="calculator">8*7*2</gadget>
<output>112</output>
112.   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  504 - 112= 
<gadget id="calculator"> 504 - 112</gadget>
<output>392</output>
392   P(couple won't sit together)= 392/504 = 7/9   The answer is 7/9.
<result>E</result>
Three people (1 couple and 1 single) are seated at random in a row of 9 chairs. What is the probability that the couple does not sit together?