Question

A function is defined by mapping f : A → B such that A contains m elements and B contains n elements and 1≤n≤m then number of onto functions are ________

(a) r=1∑^r=n ^nCr (-1)^n-r r^m

(b) r=1∑^r=n ^nCr (-1)^n-r r^n

(c) r=1∑^r=n ^nCr (-1)^m-r r^n

(d) None of the mentioned

I have been asked this question in unit test.

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

Answer 1

Correct answer is (a) r=1∑^r=n ^nCr (-1)^n-r r^m

Explanation: The number of onto function is equal tpo the coffecient of x^m in m!(e^x – 1)n.