The compound nucleus ${\mathrm{Zn}}^{64}$ was formed by bombarding ${\mathrm{Ni}}^{60}$ with $\ensuremath{\alpha}$-particles and ${\mathrm{Cu}}^{63}$ with protons. The ratios of the cross sections $\ensuremath{\sigma}(\ensuremath{\alpha},n):\ensuremath{\sigma}(\ensuremath{\alpha},2n):\ensuremath{\sigma}(\ensuremath{\alpha},pn)$ for ${\mathrm{Ni}}^{60}$ were found to agree with the ratios $\ensuremath{\sigma}(p,n):\ensuremath{\sigma}(p,2n):\ensuremath{\sigma}(p,pn)$ for ${\mathrm{Cu}}^{63}$, giving a direct verification of the theory of compound nucleus. The observed cross sections for the ($p,n$), ($p,2n$), and ($p,pn$) reactions on ${\mathrm{Cu}}^{63}$ and ($\ensuremath{\alpha},n$), ($\ensuremath{\alpha},2n$), and ($\ensuremath{\alpha},pn$) reactions on ${\mathrm{Ni}}^{60}$ have been compared with the theoretical cross sections calculated on the basis of the statistical model. The observed anomalous behavior of the ($p,pn$) and ($\ensuremath{\alpha},pn$) cross sections with respect to the ($p,2n$) and ($\ensuremath{\alpha},2n$) cross sections respectively are discussed.