Litovel Group Title stuck on a permutations question - A clerk at a bookstore is restocking a shelf of best-selling novels. He has 5 copies each of 3 different novels. How many different ways can he arrange the books on the shelf? one year ago one year ago

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1. Litovel Group Title

figured it out , 15! / 5 ! 5! 5! with cancellation

2. freewilly922 Group Title

It depends on how many books fit the shelf. If he can fit all of them on the shelf, then this is the same as the famous mississippi problem. only instead of letters you have a type of book. If he can only fit say, 3 books on a shelf, then the problem is somewhat more complicated.

3. freewilly922 Group Title

$\checkmark$

4. KiaraMarieKlinkefus Group Title

i think 6 he can arrange them 6 different ways i think

5. freewilly922 Group Title

Imagine of all 15 books were unique. you would then have 15! different combinations. for each combination, though there are 3 sets of 5! equivalencies when you take into account 3 books and 5 copies. so 15!/(5!5!5!)

6. kropot72 Group Title

If n given things can be divided into c classes of alike things differing from class to class, then the number of permutations of these things taken all at a time is: $\frac{n!}{n _{1}!n _{2}!....n _{c}!}$ where $n _{1}+n _{2}+.......n _{c}=n$ So @Litovel has the correct answer.