When a certain biased coin is flipped five times, the probability of getting heads exactly once is not equal to $$0^{}_{}$$ and is the same as that of getting heads exactly twice. Let $$\frac ij^{}_{}$$, in lowest terms, be the probability that the coin comes up heads in exactly $$3_{}^{}$$ out of $$5^{}_{}$$ flips. Find $$i+j^{}_{}$$.

(第七届AIME1989 第5题)