Question

Seven new graduates are hired by an engineering firm. Each is assigned at random to one of seven cubicles arranged in a row in the back of the room that houses the engineering staff. Two of the graduates are Bill and Cathy. What is the probability that they are assigned adjacent cubicles?

Answer 1

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:

$N = \frac{7!}{(7-7)!}=7*6*5*4*3*2\\ N=5,040\ ways$

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):

$n=2*\frac{6!}{(6-6)!} =6*5*4*3*2*2\\n=1,440\ ways$

The probability that Bill and Cathy are assigned adjacent cubicles is:

$P=\frac{n}{N}=\frac{1,440}{5,040}=0.2857$