For polynomials P(x)=a_{n} x^{n}+\cdots+a_{0}, let f(P)=a_{n} \cdots a_{0} be the product of the coefficients of P. The polynomials P_{1}, P_{2}, P_{3}, Q satisfy P_{1}(x)=(x-a)(x-b), P_{2}(x)=(x-a)(x-c), P_{3}(x)=(x-b)(x-c), Q(x)=(x-a)(x-b)(x-c) for some complex numbers a, b, c. Given f(Q)=8, f\left(P_{1}\right)+f\left(P_{2}\right)+f\left(P_{3}\right)=10, and a b c>0, find the value of f\left(P_{1}\right) f\left(P_{2}\right) f\left(P_{3}\right).