Three balls are drawn from a collection of 7 white, 12 green and 4 red balls The probability that each is of different colour

The number of balls in the collection is 7 white, 12 green and 4 red balls, total 23 balls

The random experiment is picking 3 balls at a time from the colleciton of 23 balls

Let $S$ be the sample space, $n\left(S\right)={23}_{C_3}$

Let $E$ be the event of getting 3 balls of different colour

Hence, $n\left(E\right)=7·12·4$

Therefore, 

         $\begin{array}{rcl}P\left(E\right)& =& \frac{n\left(E\right)}{n\left(S\right)}\\ & =& \frac{7·12·4}{{23}_{C_3}}\\ & =& \boxed{0.1897}\end{array}$