Question

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 (8 states)?

(Please state rule used and reasoning behind your solution)

Answer 1

a) Combination formula: Number of ways in which r items can be selected from n, nCr = n!/(r! x (n-r)!)

n = 50

r = 4

So, number of ways to select 4 states from 50 eligible states = 50C4

= 50/(4! x 46!)

= 230,300

b) Number of ways in which 4 factories can be chosen from mid-Atlantic region (8 states) = 8C4

= 8!/(4! x 4!)

= 70

P(all 4 factories will be located in the mid-Atlantic region) = Number of ways in which 4 factories can be chosen from mid-Atlantic region / Total number of ways to select 4 states from 50 eligible states

= 70/230,300

= 0.0003