Question

The total number of injective mappings from a set with m elements to a set with n elements m ≤ n is equal to :

(a) mⁿ  

(b) nⁿ

(c) (n !/n-m) !

(d) n !

Answer 1

Correct option n ! /(n -m) !

Explanation:

Let A = {a₁, a₂, … am},B = {b₁, b₂, …, bn}, and let f : A → B. The possible choices for f (a₁) are n.

Having fixed f (a₁), the possible choices for f (a₂) are n − 1, and so on. Thus, there are

n (n − 1) (n − 2) … (n − (m − 1)) = n !/(n -m) !

injective mappings from A to B.