Answer
a) $n^{m}$
b) $10^{5}$
c) n(n-1)...(n-m+1)
d) 30240
e) 0
Work Step by Step
a) According to the product rule, the number of functions, ie number of different tasks of assigning values is the product of n.n.n...$m$ times = $n^{m}$
b) 10$\times$10$\times$10$\times$10$\times$10 =$10^{5}$
c) According to the product rule, the total number of one-to-one functions is n(n-1)..(n-m+1)
d) As before one-to-one function = 6.7.8.9.10 = 30240
e) Not a single onto function is possible when its image and codomain are equal.
