700 level Combo Question - need confirmation

[san2009]

2 sizes of sticky pads. Each has 4 colors - Blue, Green, Yellow, and Purple. The pads are packed in packages that contain either 3 notepads of same size and same color or 3 notepads of same size and of 3 different colors. How many different packages of the types described are possible?
a. 6
b. 8
c. 16
d. 24
e. 32


Using the slots method - I WANT TO CONFIRM SOMETHING urgently as test is in two days

same size, same color package

number of ways the sizes can be picked for 3 pads 2*1*1 = 2
number of ways colors can be picked for 3 pads 4*1*1=4

Here is the QUESTION

In this problem, it is stated that the order of the colors doesn't matter. The reason we DON'T divide "number of ways colors can be picked for the 3 pads", which is 4 by 3! is b/c here we are picking the same color three times -- so it is essentially the same item.

However, when we get to the second pacakage...and we are picking colors...since we are picking 3 different colors for the 3 pads, we do divide by 3! b/c BGY is the same as BYG or YGB etc.

Correct?

Thanks.

[GMATGuruNY]

2 sizes of sticky pads. Each has 4 colors - Blue, Green, Yellow, and Purple. The pads are packed in packages that contain either 3 notepads of same size and same color or 3 notepads of same size and of 3 different colors. How many different packages of the types described are possible?
a. 6
b. 8
c. 16
d. 24
e. 32


Using the slots method - I WANT TO CONFIRM SOMETHING urgently as test is in two days

same size, same color package

number of ways the sizes can be picked for 3 pads 2*1*1 = 2
number of ways colors can be picked for 3 pads 4*1*1=4

Here is the QUESTION

In this problem, it is stated that the order of the colors doesn't matter. The reason we DON'T divide "number of ways colors can be picked for the 3 pads", which is 4 by 3! is b/c here we are picking the same color three times -- so it is essentially the same item.

However, when we get to the second pacakage...and we are picking colors...since we are picking 3 different colors for the 3 pads, we do divide by 3! b/c BGY is the same as BYG or YGB etc.

Correct?

Thanks.

You are correct (if I'm correctly understanding what you're saying).

All same color, same size:
4 color choices
2 size choices
4*2 = 8 possible packages.

3 different colors, all same size:
Number of ways to choose a combination of 3 colors from 4 choices: (4*3*2)/(3*2*1) = 4. (We divide by 3! because we don't care about order: BYG is the same combination as YGB. Dividing by 3! gets rid of the duplicate combinations.)
2 size choices
Multiplying, we get 4*2 = 8 possible packages.

Total possible packages = 8+8 = 16.

The correct answer is C.

Good luck on your test!