Question

The number of Onto functions, f:{a, b, c, d} to {p, q, r} , is

Answer 1

If A and B are two sets having m and n elements respectively such that 1≤n≤m then number of onto function from A to B is

∑ (-1)^{n-r n}C_r r^m r vary from 1 to n

No of elements of A = 4

No of elements of B = 3

usint this formula ∑ (-1)^{n-r n}C_r r^m r vary from 1 to n

{[(-1)^(3-1)]*³C₁*1^4} + {[(-1)^(3-2)]*³C₂*2^4{ +{ [(-1)^(3-3)]*³C₃*3^4}

= 1*3*1 + (-1)*3*16 + 1*1*81

= 3-48+81

=36