Question

Let A = {x₁ , x₂ ,......, x₇ } and B = {y₁ , y₂ , y₃ } be two sets containing seven and three distinct elements respectively. Then the total number of functions f : A → B that are onto, if there exist exactly three elements x in A such that f(x) = 1/2 , is equal to :

(1)  14.⁷C₃

(2)  16.⁷C₃

(3)  14.⁷C₂ 

(4)  12.⁷C₂ 

Answer 1

Correct option  (1) 14.⁷C₃

Explanation:

Number of onto function such that exactly three elements in x ∈ A such that f(x) = 1/2  is equal to

= 7C₃ .{2⁴ – 2}

= 14.⁷C₃