# of different binary ops. on a set S

[Unassuming]

Bear with me,

Haow mainy difffferent biiinary operarations can be dephined on the set S when it has 1,2,3 or n elementz?

Sorry I typed so wierd, I don't want anybody finding this answer.

Can I confirm with you guys/gals in here that the answer is (hopefully)

1 elem = 1,
2 elem = 2^4
3 elem = 3^9
n elem = n^(n^2)

I have never had any combo class so forgive me if I am wrong with this.

 

[tiny-tim]

Hi Unassuming!

hmm … never come across that before …

if the question means what I think it does, then I agree with you …

there are n values to be assigned to n² combinations, so it's n^n².

(I think … )