Good question - and I wonder how many people are thrown off by thinking that violet and purple are the same color and it's some sort of trick question!
This problem seems to be more about keeping organized than about "math", per se, so I'd be careful to break apart the different combinations:
Same Color, Same Size:
2 sizes * 4 colors = 8 possibilities (e.g. "small black notepads"; "large purple notepads"; etc.)
8 combinations
Different Color, Same Size
We'll definitely multiply by 2 for the two sizes, and then you can either use a combinations formula (the order doesn't matter), or just write out the possibilities:
ABC, ABD, ACD, BCD (4 possibilities)
or
N=4, K= 3: 4!/(3! * 1!) = 4
So for Different Color, Same Size, there are 4 combinations for each size * 2 sizes = 8 possibilities
Together, there are 8 combinations of same color/same size and 8 combinations of different color/same size, for a total of 16 possibilities.
Like I said, this one may be more about keeping yourself organized - if you get going on one calculation you might entirely forget about the other set of possibilities.
Brian Galvin
GMAT Instructor
Chief Academic Officer
Veritas Prep
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