Humanities reading list permutations OG quant question

GRE Quant Problem Solving
1

Hey all. Having a tough time understanding this one. I can get as far as setting up the three successful scenarios of : BBNN, BBBN, and BBBB but am unable to calculate the final answer.

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For this, it’s easier to think of what is not allowed, then calculate these piece by piece.

In total, we could have have 10!/(6! x 4!) = 210 total possible combinations of 4 books.

We are not allowed the following:

  1. 4 Novels - 6!/(4! x 2!) = 15 combinations
  2. 1 Biography, 3 Novels:
    • Combinations of 3 Novels: 6!/(3! x 3!) = 20 combinations
    • Combinations of 1 Biography: 4!(1! x 3!) = 4 combinations
    • We can pair any Novel combo with any Biography combo
    • So in total, 20 x 4 = 80 combinations of 1 Biography, 3 Novels

So, we have in total: 210 - 15 - 80 = 115 allowed combinations

Hope that helps!

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