Find all combinations of 6 items. Any order, no repeats.

[Xzavios]

This may be simple but I want to see a formula and admit I've been out of school too long to figure this one out. Although it's bugging me! I would like to see a formula, too, not just the answer.

So you have 6 items. For example ABCDEF.
You must use at least one item.
Order does not matter (ie. ABC=ACB)
They can not repeat.

So how many different combinations can I create with these items?

Thanks in advanced!

 

[mathman]

1 item - 6, 2 items - 6x5/2, 3 items - 6x5x4/(3x2), 4 items - same as 2, 5 items - same as 1, 6 items - 1.

It is basically binomial coefficients.

 

[awkward]

If you don't care to break out the number of combinations based on the number of items in each group (as done by mathman), it's even simpler. Each item either is or is not included, so there are 2^6 possibilities. But you want at least one item in each selection, so subtract 1 to account for the empty set. Solution: 2^6 - 1.

 

[Xzavios]

Thanks guys I knew it was something so simple. As a designer I don't use math much anymore although it was always one of my favorite subjects in school.

This is great because this was based on a real life situation of creating images of these groups for a client. I created 60 so I see now that I'm missing 3.

 

[CellCoree]

I would approach this problem using the principles of combinatorics. To find all possible combinations of 6 items without repeats and in any order, we can use the formula for combinations without repetition, which is nCr = n! / r!(n-r)!, where n is the total number of items and r is the number of items we want to select at a time.

In this case, n = 6 (total number of items) and r = 6 (number of items we want to select). Therefore, the formula becomes 6C6 = 6! / 6!(6-6)! = 6! / 6!0! = 6!/6! = 1.

This means that there is only 1 possible combination of 6 items without repeats and in any order. This combination would simply be all 6 items listed in any order, such as ABCDEF, ACBDEF, BACDEF, etc.

I hope this helps to clarify the problem and provide a formula to solve it. Keep in mind that combinatorics can be a complex topic, so it's always good to brush up on the basics and practice solving problems like this one.