Permutation homework question help

[CEbony]

Hi, I'm new here are need help for one of my math homework problems on permutations/combinations. I've been trying to solve this for a while but I still have no idea how to solve this problem. The rules for this problem are that 1) there is no rule stating that you must choose both a vegetable and sauce nor is there rule stating that you can only choose once and 2) the order doesn't matter (e.g. lettuce and ketchup is the same thing as ketchup and lettuce). I would really appreciate some help, thank you.

 

[Deleted member 4993]

Hi, I'm new here are need help for one of my math homework problems on permutations/combinations. I've been trying to solve this for a while but I still have no idea how to solve this problem. The rules for this problem are that 1) there is no rule stating that you must choose both a vegetable and sauce nor is there rule stating that you can only choose once and 2) the order doesn't matter (e.g. lettuce and ketchup is the same thing as ketchup and lettuce). I would really appreciate some help, thank you.

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[JeffM]

It is not a well defined problem so I can see why you have trouble starting.

Are we allowed a double order of mustard? Are we counting a double order of mustard as different from a single order of mustard?

The best you can do is give an answer based on some presumed rules such as for example multiple orders of the same extra do not count as different orders, but you can order up to 21 extras.

So how many distinct orders are there if you order none of the extras?

So how many distinct orders are there if you want to order just one extra?

Can you carry on?

 

[lex]

For each item you have 2 options - choose it or don't choose it.
There are 21 items, so: 2 [MATH]\times[/MATH] 2 [MATH]\times[/MATH] 2 [MATH]\times[/MATH] ... . ... [MATH]\times[/MATH] 2 = ? options