Your company is going to build 4 factories that will use the latest robot technology. One will make prefab buildings, another sewer systems, a third will make prefab highway overpasses, and the fourth will build shipping containers. The factories will each be in a different state, but all 50 states are eligible.

(a) In how many ways can your factories be placed among the states?

(b) If you have no idea which states will be chosen, what is the probability that all 4 factories will be located in the mid-Atlantic region?

a) 230300 ways

b) Check Explanation

Step-by-step explanation:

a) This is a combination problem,

We require how many ways 4 factories be placed among 50 states.

Mathematically, that is

⁵⁰C₄ ways = 230300 ways

b) If you have no idea which states will be chosen, what is the probability that all 4 factories will be located in the mid-Atlantic region.

This can be done in two ways

Method 1

The mid Atlantic region is one of 9 geographic divisions in the US

Probability of 1 factory being located in this geographic region = (1/9)

The probability of the 4 factories being in just this region = (probability of locating one factory in this region) ⁴ = (1/9) ⁴ = 0.0001524

Method 2

The mid Atlantic region contains only 3 out of 50 states. (New York, New Jersey, Pennsylvania)

Probability of 1 factory being located in one of the 3 stares = (3/50)

Probability of locating all four factories in one of the states in this region = (3/50) ⁴ = 0.00001296.