Six new graduates are hired by an engineering firm. Each is assigned at random to one of six 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?
Solution 15SE
Step1 of 2:
We have In a Engineering firm Six new graduates are hired and here each is assigned at random to one of six cubicles arranged in a row in the back of the room that houses the engineering staff.
The two of the graduates are Bill and Cathy.
We need to find the probability that they are assigned adjacent cubicles.
Step2 of 2:
Here, The total number of pairs of cubicles is 6C2 .
Now,
nCr=
Where,
N = 6 and r = 2 substitute in above equation we get
6C2=
= 15.
Each is equally likely to be chosen. Of these pairs, five are adjacent and they are
{(1, 2), (2, 3),(3, 4), (4, 5), (5, 6)} that is number of pairs = 5.
The probability that an adjacent pair of cubicles is selected is =
=
=
Therefore,The probability that an adjacent pair of cubicles is selected is .
Conclusion:
Therefore,The probability that an adjacent pair of cubicles is selected is .
