Question

a spinner is separated into equal sections numbered 1 through 8. the spinner is spun, and 2 coins are flipped. using the fundamental counting principle, how many total possible outcomes are there?

Explanation:

Step1: Find outcomes of spinner

The spinner has 8 sections, so there are 8 possible outcomes when spinning it.
$n_1 = 8$

Step2: Find outcomes of coin - flips

Each coin has 2 possible outcomes (heads or tails). When flipping 2 coins, by the fundamental counting principle for the coin - flips, the number of outcomes is $2\times2=4$. So $n_2 = 4$.

Step3: Calculate total outcomes

By the fundamental counting principle, the total number of possible outcomes for the combined events is the product of the number of outcomes of each event. So the total number of outcomes $N=n_1\times n_2$.
$N = 8\times4=32$

Answer:

32