Question 4002: How many ways can you order a hamburger if you can order it with or without the following items: cheese, lettuce, tomatoes, pickles or onions?
Answer by longjonsilver(2297)   (Show Source):
You can put this solution on YOUR website! 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
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