Question

A bag contains 6 ​batteries, all of which are the same size and are equally likely to be selected. Each battery is a different brand. If you select 3 batteries at​ random, use the counting principle to determine how many points will be in the sample space if the batteries are selected

Answer 1

there are 120 possible points in the sample space if we select 3 batteries at random from a bag containing 6 batteries of different brands.

Explanation:

The counting principle states that if there are n ways to do one thing and m ways to do another, then there are n x m ways to do both.

In this case, we want to determine how many ways we can select 3 batteries out of 6. Using the counting principle, we can break down the selection process into three steps:

Select the first battery. There are 6 choices for the first battery.

Select the second battery. There are 5 choices left for the second battery, since we've already selected one.

Select the third battery. There are 4 choices left for the third battery.

Using the counting principle, we can multiply the number of choices for each step to get the total number of ways to select 3 batteries:

6 x 5 x 4 = 120

Therefore, there are 120 possible points in the sample space if we select 3 batteries at random from a bag containing 6 batteries of different brands.