Combinatorics (VI)

29 Dec, 2022 at 15:21 | Posted in Statistics & Econometrics | 4 Comments

Combinatorics in .NET - Part I - Permutations, Combinations & Variations – try { } catch { } meIn my library, there are n philosophy books and six economics books. If yours truly can choose two books of each type in 150 ways, how many philosophy books are there in my library?

4 Comments

  1. I am still thinking in terms similar to diagram structures in combinatorics. Not as elegant as your calculation. (:-)

    Comment by piedmonthudson— 31 Dec, 2022 #

    • how many history books? The business history review, 1926-present is a first rate sourrce that we ignore in the rwer world.

      Comment by robert r locke— 31 Dec, 2022 #

  2. C(n,r) = n!/(r!(n-r)!)

    There are 15 combinations of 6 econ books taken 2 at a time.
    C(6,2) = 6!/(2!4!) = 30/2 =15

    That means that if x is the number of phil books, C(x,2) =10 (150/15)
    C(5,2) = 5!/(2!3!) = 20/2 = 10
    There are 5 philosophy books.

    — John Lounsbury

    Comment by piedmonthudson— 30 Dec, 2022 #

    • Right answer! My calculation, however, goes like this:
      nC2*6C2 =150 =>
      n!/(n-2)!*2 * 6!/(6-2)!*2! = n(n-1)/2! * 15 =>
      n(n-1)/2 =150/15 => n(n-1) = 20 => n^2 – n -20 = 0 => (n-5)(n+4) = 0  =>  n = 5.

      Comment by Lars Syll— 30 Dec, 2022 #


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