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Question: Let A and B be two finite sets having m and n elements respectively such that \(m \leq n\) A mapping...

Let A and B be two finite sets having m and n elements respectively such that m≤nm \leq n A mapping is selected at random from the set of all mappings from A to B. The probability that the mapping selected is an injection is

A

n!(n−m)!mn\frac { n ! } { ( n - m ) ! m ^ { n } }

B

n!(n−m)!nm\frac { n ! } { ( n - m ) ! n ^ { m } }

C

m!(n−m)!nm\frac { m ! } { ( n - m ) ! n ^ { m } }

D

m!(n−m)!mn\frac { m ! } { ( n - m ) ! m ^ { n } }

Answer

n!(n−m)!nm\frac { n ! } { ( n - m ) ! n ^ { m } }

Explanation

Solution

As we know the total number of mappings is nmn ^ { m } and number of injective mappings is n!(n−m)!nm\frac { n ! } { ( n - m ) ! n ^ { m } } .