   Chapter 1.2, Problem 22E

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# In Exercises 20-22, Suppose m and n are positive integers, A is a set with m elements, and B is a set with exactly n elements.If m ≤ n , how many one-to-one mappings are there from A to B ?

To determine

The number of one-to-one mapping from A to B. If mn and m and n are positive integers, A is a set exactly m elements, and B is a set with exactly n elements.

Explanation

A one-to-one correspondence means that each element of the codomain gets “hit” once by an element of the domain.

So let’s build maps.

The first element of A has n choices for where to map it in B, the second has n1 …, and the last has nm+1

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