Lets say a company sells 21 products

Within each product there’s the option to tailor up to and including 10 different aspects.

How many different product permutations does that create?

how many different ways can you adapt each of the 10 aspects?

How many different product permutations does that create?

Depends as you said up to 10.

or is each aspect its own variant, so 10! different versions of each product?

i.e. 10! x 21 = 76208400

or….

do you mean a product A can be
A1
A1+2
A1+2+…+10
A2
A2+3…
.
.
A2+4
etc
etc

If you mean there can be 10 different variations of each of 21 different products then theres 10^21 = 1,000,000,000,000,000,000,000 combinations

You can have any combination of the 10 options on each plan, including or excluding any that you want.

I thought 10^21 was a bit too straightforward?

OMG, OP question FAIL!

Anyway the answer is 111

… so 10! different versions of each product?

i.e. 10! x 21 = 76208400

That was my first thought

No there’s more than that

You could have product one

With 1 tailored option, which could be any one of the 10 possible
With 2 tailored options, which could be any of the 10 possible
With 3 tailored options, which could be any of the 10 possible
With 4 tailored options, which could be any of the 10 possible
With 5 tailored options, which could be any of the 10 possible

etc etc

You could have product one

With 1 tailored option, which could be any one of the 10 possible
With 2 tailored options, which could be any of the 10 possible
With 3 tailored options, which could be any of the 10 possible
With 4 tailored options, which could be any of the 10 possible
With 5 tailored options, which could be any of the 10 possible

That is 10! isn’t it?

still insufficient info.

I am revising my sweepstake answer to 5318008

That is 10! isn’t it?

No

Client A buys Product One and wants three tailored options – 1,3 & 5

Client B buys Product One and wants three tailored options – 2,4 & 6

Client C buys Product One and wants three tailored options – 3,5 & 7

etc etc

They can select any Product and any combination of tailored options

So you have 21 base products, each of which can be varied in 10 ways

21 * (1+2^10) = 55378008

EDIT sorry that should be

21 * (2^10) = 71077345

That sounds about right.

Yes, I’m off to tell the marketing team they need to make up 55,378,008 different customer handbook templates 8)

I’m changing my answer to 21504. Cynic-al, I agree with your logic, not your maths 🙂