A bag contains 4 red, 3 black and 2 white balls.

3 balls are selected at random

$n\left(S\right)={ }^9{C}_3=84$

$\mathrm{E}=\mathrm{Event} \mathrm{of} \mathrm{selecting} 3\mathrm{balls} \mathrm{which} \mathrm{contain} \mathrm{atleast} \mathrm{one} \mathrm{white} \mathrm{ball}$

$\overline{\mathrm{E}}=\mathrm{event} \mathrm{of} \mathrm{not} \mathrm{selecting} \mathrm{a} \mathrm{white} \mathrm{ball}$

$n\left(\overline{E}\right)={ }^7{C}_3=35$

$\mathrm{P}\left(\mathrm{E}\right)=1-\mathrm{P}\left(\overline{\mathrm{E}}\right)=1-\frac{35}{84}=1-\frac{5}{12}=\frac{7}{12}$