Question

A bag contains six

​batteries, all of which are the same size and are equally likely to be selected. Each battery is a different brand. If you select four

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.

Answer 1

it is asking for how many points will be in the sample space

a) with replacement, you are drawing from a total of 6 each time. you pick four batteries, so you would multiply 6 by itself 4 times
b) without replacement, you start with 6, but in each subsequent draw, you reduce the # by 1. so multiply 6 * 5 ... etc. until you get four draws.