How many one-to-one functions are there from a set with m elements to one with n elements?

I do not understand the solution

Solution:
First note that when mn there are no one-to-one functions from a set with m elements to a set with n elements...?

What does this part of the solution mean?
Why does is matter the value of the elements within the set m and n as long as it is all different numbers?

Question

How many one-to-one functions are there from a set with m elements to one with n elements?

I do not understand the solution

Solution: 
First note that when m>n there are no one-to-one functions from a set with m elements to a set with n elements...?

What does this part of the solution mean?
Why does is matter the value of the elements within the set m and n as long as it is all different numbers?

ganeshie8 · Answer

Hi

ganeshie8 · Answer

Consider the situation of 10 boys and 9 girls.

ganeshie8 · Answer

Is it possible for every boy to have exactly one girl friend ?

usukidoll · Answer

no cuz one girl will be left out

usukidoll · Answer

whoops I meant one boy will be left out

ganeshie8 · Answer

That means we cannot have one to one relationship if we have boys more than girls

ganeshie8 · Answer

Notice that we don't care if girls are left out here. Only the domain, boys, must all be paired up. There can be some girls in the codomain that don't have a preimage

anj123 · Answer

So were assuming that one set is larger than the other?

anj123 · Answer

It is example 7

anj123 · Answer

okay in the question, it says the value of the function at a(k) can be chosen in n-k+1 ways.

I understand the n-k but why did they add 1?

terenzreignz · Answer

are you still in a pinch? ^_^

sshayer · Answer

$$\left( n-0 \right)\left( n-1 \right)\left( n-2 \right)......\left\{ n-\left( m-1 \right) \right\}=n \left( n-1 \right)\left( n-2 \right)...\left( n-m+1 \right)$$