15. Use $x, y, z$ to form a six-digit permutation, requiring $x$ to appear 2 or 3 times, $y$ to appear an odd number of times, and $z$ to appear 2 times. Find the number of such permutations.
15. Consider the generating function $f(t)=\left(\frac{t^{2}}{2!}+\frac{t^{3}}{3!}\right)\left(\frac{t}{1!}+\frac{t^{3}}{3!}+\frac{t^{3}}{5!}\right) \cdot \frac{t^{2}}{2!}=\frac{t^{5}}{4}+\frac{t^{6}}{12}+\frac{t^{7}}{24}+\frac{t^{8}}{72}+\frac{t^{9}}{480}+\frac{t^{10}}{1440}=$ $30 \cdot \frac{t^{5}}{5!}+60 \cdot \frac{t^{6}}{6!}+\cdots \cdot \frac{t^{6}}{6!}$, the coefficient of $\frac{t^{6}}{6!}$ is 60, which means the permutation number is 60.