How many different ways can three cell phone covers be drawn from a box containing...

four different colored cell phone covers, if:
a. Each cell phone cover is replaced after it has been drawn? 64
b. There is no replacement? 24

I have the answers, I just don't know how to reach them. Help?

First thing : Counting Principle i.e counting without actually counting :-)
suppose u have to go from A---->B but in between there is an unavoidable C i.e the path is A--->C--->B.
and there are 3 ways to reach C from A and 2 ways to B from C. Our target is to find number of ways to get to B from A, now as for every path of A-->C (3 in number) , there are 2 paths to go further to B. So in all 3x2=6 ways A---->B "via C".

Your Ans:
a. We have to get three covers (starting from no cover).
For the first cover to draw we have four options.
For the Second cover to draw we have four options, as after drawing the first we replace the chosen cover.
For the Third cover to draw we have four options, as after drawing the second we replace the chosen cover.
So we follow:
NO COVER----4 ways--->ONE COVER CHOSEN---4 ways---->SEC COVER CHOSEN---4 ways--->THIRD COVER CHOSEN.
as all choice with replacement.

in all 4x4x4= 64 ways! by counting principle...

b. in this case we follow

NO COVER---4 ways---->FIRST COVER CHOSEN----3 ways--->SECOND COVER CHOSEN----2 ways---->THIRD COVER CHOSEN.

Each time number of ways decreased by one because we don't replace the chosen cover!!

so by counting principle: 4x3x2 =24 ways.

If replaced, there is always 4 ways. So, 4*4*4.. That is 64 ways. If not replaced, first you can have 4 chances, second you have only 3 chances and third you have only 2 chances. So,4*3*2.that is 24 ways

a. 4x 4 x 4 = 64

b. 4 x 3 x 2 = 24