If you are a genius help!!

Im having problems in this question, i have asked my friends and teachers but they dk either, please help!!

Let A = {1,2,3,4}. The number of functions f: S ---> S. Such that f(f(i) = i for all 1<= i <= 4 is?
Im getting the answer 24 (4!) by applying the condition that the function must be bijective as its inverse exists. But the answer is 10

idk if vlr is the place for this

(-demon1)+flor = winning champs

No clue how you mean you got 24.

There are 10 solutions:
The first is just f(i) = i (trivial).

Then there are 6 solutions that only flip 2 numbers such as
f(1) = 2, f(2) = 1, f(3) = 3, f(4) = 4

Finally there are 3 solutions that flip 2 pairs of numbers such as
f(1) = 2, f(2) = 1, f(3) = 4, f(4) = 3

"Flipping" numbers is the only way to have f(f(i)) = i so there are no other solutions.

tell me why u put 4! in the answer

(i) f(a) = a, f(b) = b, f(c) = c, f(d) = d ; 1 case
(ii) f(a) = b, f(b) = a, f(c) = c, f(d) = d ; 6 case
(iii) f(a) = b, f(b) = a, f(c) = d, f(d) = c ; 3 case

1+6+3 = 10 case

1+2+3+4=10

so bassicly then you and then from there you get and thats that! hope this helped

Yo, i’m what you would call a Genius

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