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

a) 64

b) 24

Step-by-step explanation:

If the number of ways to do a thing = m

and the number of ways to do another thing = n

Total number of ways of doing the two things = m * n

A ) with replacement

So far the batteries are selected with replacement. After every selection, the number of batteries becomes complete agai.

Number of ways of selecting the first battery = 4

Number of ways of selecting the second battery = 4

Number of ways of selecting the third battery = 4

Total number of ways of selecting the three batteries = 4*4*4 = 64  ways

There will be 64 points in the sample space

b) without replacement

Since the batteries are replaced after every selection:

Number of ways of selecting first battery = 4

Number of ways of selecting second battery = 3

Number of ways of selecting third battery = 2

Total number of ways of selecting the three batteries = 4*3*2=24 ways

There will be 24 points in the sample space

20%

step-by-step explanation: