​ How many onto (or subjective) functions are there from an n-element (n ≥ 2) set to a 2 -element set?

Question

How many onto (or subjective) functions are there from an n-element (n \(\geq\) 2) set to a 2 -element set? 

(A) 2ⁿ

(B) 2ⁿ -1 

(C) 2ⁿ - 2

(D) 2(2ⁿ -2)

Answer 1

(C) 2ⁿ - 2

Total number of functions is 2ⁿ, out of which t here will be exactly two functions where all elements map to exactly one element, so total number of onto functions is 2ⁿ-2