Question

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?

Answer 1

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

Answer 2

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.

Answer 3

\[\checkmark\]

Answer 4

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

Answer 5

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!)

Answer 6

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.