Final answer:
The statement is true when the two things are independent, adhering to the fundamental principle of counting in probability which implies that the number of ways to perform both actions is the product of the ways to perform each action individually.
Step-by-step explanation:
The statement If there are 'm' ways of doing one thing and 'n' ways of doing another thing, there are (m) x (n) ways of doing both is True if the things are completely independent of each other. This follows the fundamental principle of counting in probability, which states that if there are m ways of doing one thing and n ways of doing another, and the two things don't interfere with each other, then there are m x n ways of doing both.
For example, if a person has 3 different shirts and 4 different pairs of pants, then that person has 3 x 4 = 12 different possible shirt and pant combinations. Here the choice of shirt does not affect the choice of pants, making the events independent. However, if the events were not independent (mutually exclusive), then the calculation might be different.