We have,

$4$ red balls

$5$ blue balls

$6$ yellow balls

Favourable outcomes are

$\mathrm{RBY}, \mathrm{RYB},\mathrm{BRY},\mathrm{BYR},\mathrm{YRB},\mathrm{YBR}$

Required probability

$=\left(\frac{4}{15}\times \frac{5}{14}\times \frac{6}{13}\right)+\left(\frac{4}{15}\times \frac{6}{14}\times \frac{5}{13}\right)+\left(\frac{5}{15}\times \frac{4}{14}\times \frac{6}{13}\right)+\left(\frac{5}{15}\times \frac{6}{14}\times \frac{4}{13}\right)+\left(\frac{6}{15}\times \frac{4}{14}\times \frac{5}{13}\right)+\left(\frac{6}{15}\times \frac{5}{14}\times \frac{4}{13}\right)$

$=\frac{4}{15}\times \frac{5}{14}\times \frac{6}{13}\times 6$

$=\frac{24}{91}$