you spin the spinner, roll a die, and flip a coin. how many outcomes are possible?

Answer

Explanation:

Step1: Determine spinner outcomes

The spinner has 2 outcomes (either B or C), so $n_1 = 2$.

Step2: Determine die - roll outcomes

A die has 6 faces, so there are 6 possible outcomes, $n_2=6$.

Step3: Determine coin - flip outcomes

A coin flip has 2 possible outcomes (heads or tails), $n_3 = 2$.

Step4: Use the multiplication principle

The total number of possible outcomes for the combined events is the product of the number of outcomes of each individual event. So the total number of outcomes $N=n_1\times n_2\times n_3$. Substitute $n_1 = 2$, $n_2=6$, and $n_3 = 2$ into the formula: $N=2\times6\times2$. $N = 24$.