SOLUTION: There are 8 different foods in the refrigerator. How many different ways can we take 3 of them to make a meal, if the order of the items eaten is not important? If the order of

Question 1051667: There are 8 different foods in the refrigerator. How many different ways can we take 3 of them to make a meal, if the order of the items eaten is not important?
If the order of the 3 different foods eaten is important?
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
combination formula if order is not important.
permutation formula if order is important.

combination formula is c(n,x) = n! / (x! * (n-x)!)

permutation formula is p(n,x) = n! / (n-x!).

n = 8
x = 3

c(n,x) = 8! / (3! * 5!) = (8*7*6*5!) / (3*2*1*5!) = (8*7*6) / (3*2*1) = 56

p(n,x) = 8! / (5!) = (8*7*6*5!) / 5! = (8*7*6) = 336

the difference is the 3!.

when order is important, the same elements can exist in different sets, but in different order.

example:
ab is one set where order is not important.
the elements are unique in that set but the order they are arranged in that set doesn't matter.
it doesn't matter if they're arranged as ab or ba.
it's still one set just as long as the elements contained in that set are in that set only.

ab and ba are two sets where order is important.
the elements are the same in both sets but the order is different.

here are two sets where order is not important.
ab is one set and bc is another set.

they're unique because at least one of the elements in each set is different.

b is common to both sets but a is only only in the first set and c is only in the second set.

the two sets where order is not important are ab and bdc

they become 4 sets when order is important, namely ab, ba, bc, cb.

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