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Combinatorics: Choosing Books on a Shelf

  • Thread starter Shoney45
  • Start date
  • #1
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Homework Statement


Given nine different English books, seven different French books, and five different German books: How many ways are there to mak a row of three books in which exactly one language is missing?




Homework Equations



P(n,k) C(n,k)

The Attempt at a Solution



I broke this up into six cases: Let English books be represented by E, German books by G, and French books by F. My six cases then are:

(2E)F = p(9,2)*7 = 504
(2E)G = p(9,2)*5 = 360
(2F)E = p(7,2)*9 = 378
(2F)G = p(7,2)*5 = 210
(2G)E = p(5,2)*9 = 540
(2G)F = p(5,2)*7 = 420

all of which equals 2412 possibilities.
 

Answers and Replies

  • #2
tiny-tim
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Hi Shoney45! :smile:
Given nine different English books, seven different French books, and five different German books: How many ways are there to mak a row of three books in which exactly one language is missing?

(2E)F = p(9,2)*7 = 504
(2E)G = p(9,2)*5 = 360
(2F)E = p(7,2)*9 = 378
(2F)G = p(7,2)*5 = 210
(2G)E = p(5,2)*9 = 540
(2G)F = p(5,2)*7 = 420
The order of the books doesn't matter, so it's not p. :wink:

(and where did your 60 come from in the last two? :confused:)
 
  • #3
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Hi Shoney45! :smile:


The order of the books doesn't matter, so it's not p. :wink:

(and where did your 60 come from in the last two? :confused:)
Sorry, but I don't understand what you mean by the 60 in my last two.

Never mind. I just figured out what you meant. That was just bad arithmetic.
 

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