Combination question: selections of fruits for mixed salads

user456123

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I vaguely remember my combination and permutation math from many years ago. I have a real-world problem to solve which can be simplified as follows. Lets say I have 5 different types of fruits and I can combine them into a fruit salad using 1 or more combinations, e.g.:

apples
apples + oranges
apples + grapes
apples + oranges + grapes
oranges + grapes
...

How many different combinations will I have in total? Order is irrelevant.
 
I have 5 different types of fruits and I can combine them into a fruit salad using 1 or more combinations, e.g.:

apples
apples + oranges
apples + grapes
apples + oranges + grapes
oranges + grapes
...

How many different combinations will I have in total? Order is irrelevant.
When you say "1 or more combinations", do you mean "combinations of 1 or more items"? If so:

In how many ways can you combine 1 of 5? (Plug into the formula to verify your answer.)

In how many ways can you combine 2 of 5? Three of 5?

After finding the values for each case, and because the different cases are disjoint (you can't have exactly two ingredients and also have exactly four), add the numbers of options for each case. This gives you the total number of options. ;)
 
I vaguely remember my combination and permutation math from many years ago. I have a real-world problem to solve which can be simplified as follows. Lets say I have 5 different types of fruits and I can combine them into a fruit salad using 1 or more combinations, e.g.:
apples
apples + oranges
apples + grapes
apples + oranges + grapes
oranges + grapes
...
How many different combinations will I have in total?

You may find this webpage useful. Frankly most of us reject the notation (()).

To put N identical objects into K different cell, there are \(\displaystyle \dbinom{N+K-1}{N}=\dfrac{(N+K-1)!}{(K-1)!(N!)}\)

In your question I would use N=5 & K=5. That way you have a constant volume from 5 parts.
 
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