<p>Hey guys i've been working through my 2008 Barron's practice book, and it has been very helpful; however, i have noticed quite a few egregious errors. Most are so blatant that it is obvious they are wrong, but i am not sure about this one problem</p>
<p>"M & M plain candies come in six colors: brown, green, orange, red, tan, and yellow. Assume there at least 3 of each color. If you pick three candies from a bag, how many color possibilities are there?"</p>
<p>a) 18
b)20
c)120
d)216
e)729</p>
<p>The answer key says D) 216. It claims that you just have to multiply 6<em>6</em>6. I think that is wrong though because that does not account for repeat color combinations. It does not distinguish Red, Red, Green from Red, Green, Red. Did the book forget to exclude repetitions or am i just reading too much into the problem? Are there many ambiguous questions like this on the actual test?</p>
<p>Actually, 216 <em>does</em> count RRG and RGR separately. Imagine you were picking only two m&m's. There are 6 * 6 orderings, and that counts, e.g., RG and GR as distinct possibilities. If you did <em>not</em> want to distinguish RG vs GR, you would have to divide by 2, to get 18 possibilities. You can check by writing all 36 down on paper. In the case of three, you would have to divide by 3! = 6, for a total of 36 possibilities.</p>
<p>I don't think this question would qualify to be on the real test: the CB/ETS tries pretty hard to ensure there aren't two different ways to read a question. The problem with the Barrons Q is that it doesn't say "orderings" or something that would have made it clear.</p>
<p>ah, thanks for clarifying. I see that i contradicted myself in my original post, but what i really meant was that 216 DID include RRG and RGR and that i thought the correct answer SHOULDNT. Thanks for describing both methods and for your input on why it wouldnt be on the test</p>