Maths problem

[MistySkiesAreGone]

Can the folk of mumsnet help me out with this?

I have 27 swatches of colours, and I want to put them together into groups of 3, and I want to do all the possible combinations of groups of 3.

Can anyone tell me how many combinations that is going to be (and how you work it out, out of interest 🤔 )

Virtual hoorah to the person who tells me as this is doing my head in. I need to figure out how much time it would take and if it's worth it!

Thanks

Does the order matter? Ie is red orange green a different group from green orange red?

I think you have 27 choices for the first colour, then 26 choices for the second colour (as you've used one) and 25 choices for the third colour. So you could make 27 x 26 x 25 different groups of three. So 17,550 different groups. (could be wrong, maths isn't my forte...)

Googled it and got this. the solutions is what looks to me like a complicated equation

There are 2925 ways that 3 items chosen from a set of 27 can be combined.

Basically, don't do it 🤣

When Rishi said we all need to study Maths until 18, someone should have told him about the answer machine called Google 😂

A level maths is calling…from a few decades ago you want to do 27 choose 3. It’s the nCr function on a calculator. And is indeed 2925 ways.

@TwitTwoodiniEscapeOwlogist and @Summerof22 are both right 😆

It’s 17550 if the order matters (27x26x25). If the order doesn’t matter (so red orange green and green orange red don’t count as different combinations) you then divide by 6 (the number of ways to arrange a group of 3) which gives 2925.

You are all geniuses!

The order doesn't matter at this stage.
But might later on.

I was thinking it could be 27, 26, 25 etc. but that seemed a dauntingly high number (which it is 😂). And the order was stumping me but I couldn't quite grasp that.

Can I complicate it?

I don't want to do all the combinations. Lets say they are all different colour. I've got 9 colours that I want to start with (the order doesn't matter, maybe read that as include) and I want to try all the combinations with those 9 colours.

So 9 colours to include, 27 in total.
My brain just can't compute it.

I think its 17 options for each colour, x 9 colours = 153