Combinations Question

GRE Quant Problem Solving
1

Hi All,

I was doing one of the hard quizzes by Gregmat and found the following question:

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I got an answer of 63, in comparison to the answer of 45. The answer of 45 was found by adding the number of side dishes (2 to the 4, or 16, minus 1 for the case where you said no to each) to the number of main dishes (2 to the 2, or 4, minus 1, to get to 3) and then multiplying them together to get 45.

The answer I got was by taking the total number of choices, 6, and making the all yes and no questions, to get 64, and then subtracting the 3 cases where you chose no (either no for a side dish, no for a main course, or no for both), to get 61. I was hoping someone may be able to guide me here as to what I missed as I was fairly confident my answer was correct?

Have a great rest of your day!

2

Let 1 denote a “yes” and 0 denote a “no.

Moreover, let the first 4 slots be for main dishes and the last 2 for side dishes, so you’re looking at something like this:

1 1 1 1 0 1

(this means you said “yes” to 4 main dishes and 1 side dish)

With that out of the way, you’re not counting all cases which doesn’t work:

For example,

Consider having all 0’s, which doesn’t work so that’s 1 invalid way

Now, consider having one copy of 1, so something like

0 0 0 0 1 0

This don’t work, and so doesn’t all permutations of this. Thus, you get 6 more invalid configurations to remove from your total cases.

Keep working in this fashion and you’ll arrive at 45.