Question

joey has 5 different colored marbles and a 6 sided die. if joey chooses one marble and rolls the die once, how many possible combinations of marbles and dice numbers are possible? a 30 b 11 c 36 d 25

Explanation:

Step1: Identify number of choices for each action

For choosing a marble, there are 5 different colored marbles, so 5 choices. For rolling the die, a 6 - sided die has 6 possible outcomes, so 6 choices.

Step2: Apply the multiplication principle

The multiplication principle of counting states that if there are \(m\) ways to do one thing and \(n\) ways to do another thing, then there are \(m\times n\) ways to do both things. Here, \(m = 5\) (choices for marbles) and \(n=6\) (choices for die rolls). So the total number of combinations is \(5\times6\).

$$5\times6 = 30$$

Answer:

30 (corresponding to option A. 30)