# Combinatorics: Choosing Books on a Shelf

## 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?

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.

tiny-tim
Homework Helper
Hi Shoney45! 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. (and where did your 60 come from in the last two? )

Hi Shoney45! The order of the books doesn't matter, so it's not p. (and where did your 60 come from in the last two? )

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.