Question

A function is defined by mapping f : A → B such that A contains m elements and B contains n elements and m ≤ n then number of one one functions are _________

(a) ^nCm x m!

(b) ^nCm x n!

(c) 0

(d) none of the mentioned

I got this question by my college director while I was bunking the class.

The above asked question is from Number of Functions in section Basic Structures: Sets, Functions, Sequences, Sums and Matrices of Discrete Mathematics

Answer 1

Correct choice is (a) ^nCm x m!

For explanation: From n elements in B we need to select m elements and then arrange them in all ways, thus  answer=^nCm x m!.