A bag contains eight batteries, all of which are the same size and are equally likely to be selected. Each battery is a different brand. If you select two batteries at random, use the counting principle to determine how many points will be in the sample space if the batteries are selected without replacement.

Answer:

7*6*5*4*3 = 7P5 = 2520

Step-by-step explanation:

There will be 56 points in the sample space when two batteries are selected without replacement from the bag.

To determine the number of points in the sample space when selecting two batteries without replacement, we can use the counting principle.

The counting principle states that if there are m ways to do one task and n ways to do another task, then there are m * n ways to do both tasks together.

In this case, the first battery can be selected in 8 ways (since there are 8 batteries in the bag).

After selecting the first battery, there are 7 remaining batteries in the bag. For the second battery, there are 7 ways to select it (one less than the previous selection).

Therefore, the number of points in the sample space is given by multiplying the number of possibilities for the first selection (8) by the number of possibilities for the second selection (7):

8 * 7 = 56

There will be 56 points in the sample space when two batteries are selected without replacement from the bag.

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