# Math Help - number of bijection from A to B

1. ## number of bijection from A to B

Let A and B be sets such that |A|=|B|=m. What is the number of bijections from A to B?

2. Originally Posted by santiagos11
Let A and B be sets such that |A|=|B|=m. What is the number of bijections from A to B?
Hint:
Spoiler:
Permutation

3. never mind I got it. Suppose |A|=|B|=m. Then we have a bijection iff we have injection. Since there are m! injections, we have m! bijections.

4. Originally Posted by santiagos11
never mind I got it. Suppose |A|=|B|=m. Then we have a bijection iff we have injection. Since there are m! injections, we have m! bijections.
Or! You can note that a bijection and a permutation are in fact the same (for finite cases...the infinite case holds but with a slightly different meaning). Thus, how many ways are there to permute $m$ objects? [tex]m![/math\