Let `n(A)=5` and `n(B)=3` then find the number of injective functions and onto functions from `A ` to `B`

Explanation

We know that in onto mapping, each image must be assigned atleast one pre-image.
This is equivalent to number of ways in which 5 different balls (pre-images) can be distributed in 3 different boxes (images), if no box remains empty. The toal number of onto mappings from A to B.
`=3^(5)-.^(3)C_(1)(3-1)^(5)+.^(3)C_(2)(3-2)^(5)`
`=243-96+350`