Question 844896
Look at all of the combinations that don't have R in them and calculate the probabilities
{{{BBB=4*4*4/12^3=64/1728}}}
{{{BBG=4*4*5/12^3=80/1728}}}
{{{BGB=4*5*4/12^3=80/1728}}}
{{{BGG=4*5*5/12^3=100/1728}}}
{{{GBB=5*4*4/12^3=80/1728}}}
{{{GBG=5*4*5/12^3=100/1728}}}
{{{GGB=5*5*4/12^3=100/1728}}}
{{{GGG=5*5*5/12^3=125/1728}}}
.
.
.
{{{P(at least 1 R)+P(no R)=1}}}

{{{P(no R)=(64+3*80+3*100+125)/1728=729/1728}}}
{{{P(at least 1 R)=1-729/1728}}}
{{{P(at least 1 R)=999/1728}}}
{{{P(at least 1 R)=111/192}}}