Question

The state of Georgia is divided up into 159 counties. Consider a population of Georgia residents with mutually independent and equally likely home locations. If you have a group of n such residents, what is the probability that two or more people in the group have a home in the same county

Answer 1

Answer:

$\frac{159^{n} -(\left \{ {{159} \atop {n}} \right.)*n! ) }{159^{n} }$

Step-by-step explanation:

number of counties = 159

n number of people are mutually independent and equally likely home locations

considering the details given in the question

n ≤ 159

The number of ways for people ( n ) will live in the different counties (159) can be determined as $(\left \{ {{159} \atop {n}} \right} )$

since the residents are mutually independent and equally likely home locations hence there are : $159^{n}$ ways for the residents to live in

therefore the probability = $\frac{159^{n} -(\left \{ {{159} \atop {n}} \right.)*n! ) }{159^{n} }$