Question

What are the limitations of the fundamental counting principle? And what is an example?

a) The fundamental counting principle cannot be applied to probability calculations.
b) The fundamental counting principle assumes that all outcomes are equally likely.
c) The principle is limited when dealing with dependent events.
d) The principle is limited to permutations, not combinations.

Answer 1

The limitations of the fundamental counting principle include its inability to be used in probability calculations, assumption of equally likely outcomes, limitations with dependent events, and its restriction to permutations instead of combinations.

Step-by-step explanation:

The fundamental counting principle, also known as the multiplication rule, has a few limitations:

1. The fundamental counting principle cannot be applied to probability calculations. In probability, the multiplication rule and addition rule are used instead.
2. The fundamental counting principle assumes that all outcomes are equally likely. This may not be the case in real-life scenarios.
3. The principle is limited when dealing with dependent events. When events are dependent, the outcomes of one event affect the outcomes of another event, and the fundamental counting principle may not be applicable.
4. The principle is limited to permutations, not combinations. Permutations are arrangements where order matters, while combinations are selections where order does not matter.

An example of the limitation of the fundamental counting principle is calculating the number of ways to select two cards from a deck of cards. If the order of selection matters, it is a permutation problem. If the order does not matter, it is a combination problem.