a A cafteria has 23 food items available If you are going to

a) A cafteria has 23 food items available. If you are going to compose the lunch of four items, how many ways can your lunch be chosen? My question is: is this a permuation or combination problem? I think it\'s combination but I\'d appreciate if you could explain how to tell the difference.

b) If you assigned a number to (10 over 11) what should it be? Note: the 10 is directly over the 11 with no divisor and both are inside the parentheses, so it\'s clear this is a combination. I\'m just not sure what the number should be.

I awarded extra points because I know there\'s a lot of explaining to do on these two questions :) Thanks for your help!

Solution

23 items out of which you choose 4

Since choosing ABCD is the same as ABDC or ACBD or DBCA etc, the order does not matter here

And therefore, this is a combination

Where the order matters, it is a permutation
Where the order does not matter, that is a strict combination

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That is basically 10 C 11, which in layman\'s terms is :

The number of ways of choosing 11 items from 10 items

The fact that we have a total of 10 items makes it impossible to choose 11 items, right?

So, we cna simply say that the number of ways of choosing 11 from 10 is : 0 ways

So, the number you assign to it is : 0 --> ANSWER