Question

# How many onto functions can be defined from the set A = {1, 2, 3, 4} to {a, b, c}

A
B
C
D
##### 45
Solution

Correct option is

(C)

If a set A has m elements and set B has n elements, then the number of onto functions from A to B = $n^{m}-nC_{1}(n-1)^m+nC_{2}(n-2)^m-nC_{3}(n-3)^m$
so,$3^{4}-3C_{1}(3-1)^4+3C_{2}(3-2)^4-3C_{3}(3-3)^4$