$14 \cdot 33$ Given six points on a circle, the probability that four randomly chosen chords form a convex quadrilateral is
(A) $\frac{1}{15}$.
(B) $\frac{1}{91}$.
(C) $\frac{1}{273}$.
(D) $\frac{1}{455}$.
(E) $\frac{1}{1365}$.
(50th American High School Mathematics Examination, 1999)
[Solution] The total number of chords that can be connected by the given six points is $C_{6}^{2}=15$; the number of ways to choose four chords from these is $C_{15}^{4}$.

According to the problem, the number of convex quadrilaterals that can be formed by the chords connecting the six points is $C_{6}^{4}$. Therefore, the required probability is
$$
P=\frac{C_{6}^{4}}{C_{15}^{4}}=\frac{1}{91} .
$$

Thus, the correct choice is (B).