A) \[14.{{\,}^{7}}{{C}_{2}}\]
B) \[16.{{\,}^{7}}{{C}_{3}}\]
C) \[12.{{\,}^{7}}{{C}_{2}}\]
D) \[14.{{\,}^{7}}{{C}_{3}}\]
Correct Answer: D
Solution :
Selection of three element in A such that \[f\left( x \right)={{y}_{2}}{{=}^{7}}{{C}_{3}}\] Now for remaining 4 elements in A we have 2 elements in B \[\therefore \]Total number of onto function \[{{=}^{7}}{{C}_{3}}\times \left( {{2}^{4}}-2{{C}_{1}}{{\left( 2-1 \right)}^{4}} \right){{=}^{7}}{{C}_{3}}\times 14\]
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