If function f(x) is defined from set A to B, such that `n(A)=3` and `n(B)=5`. Then find the number of one-one functions and number of onto functions that can be formed.

Explanation

For one-one function each preimage in set A must have distinct image in set B.
So, number of one-one functions from set A to B
= number of permutations of five objects (images) taken three (preimages) at a time
`=""^(5)P_(3)=5xx4xx3=60.`
For onto function each image must have pre-image.
Now consider three elements of set A as three distinct boxes and five elements of set B as five distinct objects.
Number of onto functions from set A to B
= number of ways five distinct objects can be distributed into three boxes so that no box remains empty
`=3^(5)-""^(3)C_(1)(3-1)^(5)+""^(3)C_(2)(3-2)^(5)`
`=243-96+3`
`=150`