Question 4002
1. you can have 1 item only --> 5 possibilities

--> mathematically, this is worked out by 5!/1!4!


2. you can have 2 items --> cheese with one of the other 4 items. lettuce with one of the other 3 items (not cheese, as that has been done), tomatoes with one of the other 2 items and then pickles with just onions. This totals 10 combinations

--> this is 5!/3!2!


3. you can have 3 items:
ABC ACD ADE
ABD ACE 
ABE

BCD BDE
BCE

CDE


--> Again totalling 10 --> 5!/3!2!


4. you can have 4 items:

ABCD ACDE BCDE
ABCE ABDE

Totalling 5 combinations --> 5!/4!1!


5. you can have 5 items --> total of 1 occurrence.


So, total different ways is: 5 + 10 + 10 + 5 + 1 = 31


jon