Take the 2-minute tour ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

let us consider this problem:

Chelsea has a bookshelf consisting of ten classics: four Russian novels, three British novels, two French novels, and a German novel. If she wants to make sure that the novels are always grouped according to country, how many ways can she arrange the novels?

my attempt is following because these novels should be arranged according to country,it means that i should multiply number of arrangement of Russian novels together by number of British novels arrangement by French and one German Novels number of arrangement,which means that

$4!*3!*2!*1!=288$

but in answer there is $24*288=6912$ where $24$ comes from?does it means that there is $24$ ways first book i could choose? $4*3*2*1=24$?

share|improve this question

1 Answer 1

up vote 2 down vote accepted

Consider the big group. So you have Russian, British, French, and German. You can arrange them $4!$ ways. For each type of book, you can arrange them $4!$, $3!$, $2!$, and $1!$ ways (which is what is in your attempt.)

So the final answer is $4!4!3!2!1!=6912$.

share|improve this answer
1  
it means that $4!$ is related to number of country,not number of books right? –  dato datuashvili Aug 1 '13 at 6:01
    
and also it means that order is important right? –  dato datuashvili Aug 1 '13 at 6:11
1  
yes, $4!$ refers to the country, and the order matters. –  vantonio1992 Aug 1 '13 at 12:02

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.