**Correct option (d) ****14⋅( **^{7}C_{3})

**Explanation :**

We have A = {x_{1}, x_{2}, x_{3}, … x_{7}} and B = {y_{1}, y_{2}, y_{3}}. 3 elements in A having image y_{2} can be chosen in ^{7}C_{3} ways. Now we are left with 4 elements in A which are to be associated with y_{1} or y_{3 }i.e. each of 4 elements in A has 2 choices y_{1} or y_{3} i.e. in (2)^{4} ways. But there are 2 ways when one element of B will remain associated i.e. when all 4 are associated with y_{1} or y_{3}.

Therefore, required number of functions =^{ 7}C_{3}((2)^{4} - 2)

= 14⋅( ^{7}C_{3}) .