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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.