question_answer

Let F denotes the set of all onto functions from \[A=\{{{a}_{1}},\,\,{{a}_{2}},\,\,{{a}_{3}},\,\,{{a}_{4}}\}\] to \[B=\{x,\,\,y,\,\,z\}\]. A function f is chosen at random from F. The probability that \[{{f}^{-1}}(x)\] consists of exactly two elements is _____.

A)  0                                

B)  \[\frac{1}{3}\]

C)  \[\frac{1}{6}\]                         

D)  \[\frac{2}{3}\]

E)  None of these