Ten books are to be placed on a shelf.

Question

Three of the books are identical. Two others also match, but are different from the three identical ones. The other five books are each unique. How many different ways are there to shelve the books?

Answer 1

If all were distinct (different), it would be a permutation of ten things taken 10 at a time, i.e. 9!

 

But when there are two subgroups that appear identical, (one of 3 identical books and another of 2 identical books), this number must be divided by the product 3!2!

 

Therefore your answer is 30240.