Question

Distributions of Distinct Objects to Distinct Recipients and using the principle of inclusion-exclusion:

Let X={1,2,3,...,8 } and Y={a,b,c,d,e}.
a) Count the number of surjections from X to Y.
b) Count the number of functions from X to Y whose image consists of exactly three elements of V.

Answer 1

a)

Let m,n be two integers such that, m≥n

Compute the number of surjections from {1,...,m} to {1,...,n}

m = 8 , n = 5
|S| = 5^8 - 5 4^8 + 10 3^8 -10 2^8 + 5