Can we map this problem to subset-sum?

Let there be $$n$$ set of ordered pairs
$$s_1=\{(c_1,f_1),(c_1,f_2) ...(c_1,f_m)\}$$,
$$s_2=\{(c_2,f_1),(c_2,f_2) ...(c_2,f_m)\}$$,
$$s_3=\{(c_3,f_1),(c_3,f_2) ...(c_3,f_m)\}$$,
....
$$s_n=\{(c_n,f_1)(c_n,f_2) ...(c_n,f_m)\}$$

and

$$T((c,f))$$ be a function that takes an ordered pair or element of the sets and returns a positive rational number.

can we select one element each from all the $$n$$ sets such that $$\sum T((c_i,f_j)) =T$$ where $$\bigcap_{i=1}^{n } c_i =\phi$$

• I think that the question tries to be that we need to select a transversal, i.e., at most one element from each column. Am I right? – domotorp Jul 16 at 16:31
• @domotorp yes that would be one way to put it – AVIK DUTTA Jul 16 at 16:35
• Well, I really don't think this question belongs here, it does look too easy. – domotorp Jul 16 at 19:57