How many ways to combine 4 numbers?

Question

Hi,

If you have a set, {a,b,c,d) how to you calculate the number of different combinations, and what are they?

I thought it was 4^2 = 16 but now I am not so sure...

Thanks.

Answer 1

It depends on what you mean by "combine".

There are 2^4 = 16 distinct subsets of {a,b,c,d}, including the entire set and the empty set.

There are 4^2 = 16 different (x,y) pairs you can make.

There are 4! = 24 different orders they can be put in (i.e. abcd, bcad, dcba, etc.).

Is one of these what you're asking for?

Answer 2

Yes, two are missing from the list. There should be 6 for each starting number. So, we find missing the two others that start with the number 3. They are, 3412 and 3421.

4! = 24 and 3! = 6 - the answer to 3! give you the best clue to what's missing in the original list.

Answer 3

If you have 4 numbers and you want to combine them into a combination of 4 numbers where repeating doesn't matter:
4^4 = 256

If repetition does matter:
4! = 4*3*2*1 = 24

Answer 4

It is 4!=24.
for the first place you have 4 opportunities, for the second 3 etc.

Answer 5

It's 16.
Example-
For A-
ABCD
ACBD
ADBC
ACDB

Answer 6

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