Question

Indicate whether the Fundamental Counting Principle applies to this situation: Counting the number of possibilities to choose from when buying a bicycle available in 4 sizes and 3 colours. Explain using the definition of the Fundamental Counting Principle and then provide a counter example.

Answer 1

The Fundamental Counting Principle does apply to counting the number of possibilities for bicycle sizes and colours, which results in 4 x 3 = 12 different combinations. A counter example would involve dependent outcomes, where the principle might not apply accurately.

Step-by-step explanation:

The Fundamental Counting Principle does apply to situations like counting the number of possibilities when buying a bicycle available in 4 sizes and 3 colours. According to the Fundamental Counting Principle, if one event can occur in m ways and a second independent event can occur in n ways, then the total number of ways the two events can occur is m times n. In this case, a bicycle can be chosen in 4 sizes and 3 colours, which means there are a total of 4 x 3 = 12 different combinations of bicycles to choose from.

A counter example where the Fundamental Counting Principle does not apply could be when the outcomes are not independent. For instance, if a bicycle comes in 3 colours but the largest size is only available in 1 colour, the straightforward application of the principle would give a misleading result.