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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 ________

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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 had been asked this question during an internship interview.

My query is from Number of Functions topic in portion Basic Structures: Sets, Functions, Sequences, Sums and Matrices of Discrete Mathematics

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The correct choice is (c) 0

Easy explanation: Since for function to be defined every element should have a image, since m > n atleast one element need to have same image, thus we can’t form any unique images and hence the number of one one function are zero.

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