2. 2 ( from 2 types of cones) * 15 ( 15 flavors ) = 30
3. Assuming the customer can only rent one video/dvd, 16. There are 16 distinct choices as there are 8 titles and 2 format for each title.
4. We split into two disjunct cases:
the dictionary is on the far right
and the dictionary is on the far left.
If the dictionary is on the far right, than there are 5 books to permute on the left of it.
Consider this diagram: A1 A2 A3 A4 A5 D.
If we consider the possible books to put into each spot A1 to A5, there are 5! possible arrangements. 5 possible books to put into A1, 4 possible books left to put into A2 (after already putting a book in A1), 3 in A3, 2 in A4, 1 in A5. Hence 5!.
Now we consider the second case, where the dictionary in on the far left. By a very similar argument as the one above, there is another 5! possible arrangements.
Now as Case 1 and Case 2 are disjunct we can simply add their two arrangements together, so 5! + 5! = 2* 5! = 5*4*3*2*2 = 240