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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 bijections 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 bijections are ________

(a) ^nCm x m!

(b) ^nCm x n!

(c) 0

(d) none of the mentioned

This question was addressed to me by my college professor while I was bunking the class.

This interesting question is from Number of Functions topic in section Basic Structures: Sets, Functions, Sequences, Sums and Matrices of Discrete Mathematics

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Right option is (c) 0

Easiest explanation: Since we can’t define any one one function in such case so number of bujections will be zero.

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