Question

The number of bijective function f (1,3,5,7,......,99) → (2,4,6,8,.....,100) if f(3) ≥ f (5) ≥ .... ≥ f (99) is

(a) ⁵⁰C₁

(b) ⁵⁰C₂

(c) 50!/2

(d) ⁵⁰C₃ x 3!

Answer 1

Correct option is (a) ⁵⁰C₁

Bijective function means one-one and onto.

That means for every input unique output which is non-repeating so, set(1,3,5,7,.....99) 

has 50 elements and set B (2,4,6,.....100) has 50 elements.

such that f (3) ≥ f (5) ≥ ... ≥ f (99)

This can be done in ⁵⁰C₁ ways