3. For all $m, n$ satisfying $1 \leqslant n \leqslant m \leqslant 5$, the number of different hyperbolas represented by the polar equation $\rho=\frac{1}{1-\mathrm{C}_{m}^{n} \cos \theta}$ is
(A) 15
(B) 10
(C) 7
(D) 6
(D)
3.【Analysis and Solution】The polar equation of the conic section $\rho=\frac{p}{1-e \cos \theta}$ represents a hyperbola if and only if $e>1$. Therefore, the equation in this problem must satisfy $\mathrm{C}_{m}^{n}>1$. Given $1 \leqslant n \leqslant m \leqslant 5$, we can obtain 6 different values: $\mathrm{C}_{3}^{1}, \mathrm{C}_{3}^{2}, \mathrm{C}_{4}^{1}, \mathrm{C}_{4}^{2}, \mathrm{C}_{5}^{1}$, $\mathrm{C}_{5}^{2}$. Thus, there are 6 different hyperbolas.