|A|=5 |B|=3
total no of one one function =5P3=60
{a1,a2,a3} ===> {b1,b2,b3,b4,b5}
pth element map to pth eleement in n ways
n=n(A)+n(B)+n(C)-n(A ∩B)-n(B∩C)-n(C∩A) +n(A∩B∩C)
where A= a1 mapped to b1
B=a2 mapped to b2
C=a3 mapped to b3
no of ways in which a1 is mapped to b1=4P2=12 [ a1 -> b1 left combination {a2,a3}--->{b2,b3,b4,b5} ]
similarly for a2 and a3=12
A∩B= a1 and a2 mapped to b1 and b2 respectively so left possible combination {a3 to {b3,b4,b5)) i.e 3P1=3
similarly B∩C,C∩A=4
so n=12 + 12 + 12 - 3 - 3 - 3 + 1
=28
no of ways in which pth elemement not mapped to pth = 60-n=60-28=32