Answer:
0.2857
Step-by-step explanation:
The total number of ways that the seven new graduates can be seated is given by a permutation of placing 7 people in 7 spots:
[tex]N = \frac{7!}{(7-7)!}=7*6*5*4*3*2\\ N=5,040\ ways[/tex]
In order for them to sit together, consider Bill and Cathy as a single 'block', the new number of ways to seat the graduates is given by a permutation of placing 6 people in 6 spots multiplied by 2 (Bill and Cathy switching spots):
[tex]n=2*\frac{6!}{(6-6)!} =6*5*4*3*2*2\\n=1,440\ ways[/tex]
The probability that Bill and Cathy are assigned adjacent cubicles is:
[tex]P=\frac{n}{N}=\frac{1,440}{5,040}=0.2857[/tex]
