Question

A bucket contains 10 balls.  3 are red, 4 are blue and 3 are green?  If you randomly choose 5 balls without replacing any of them, what is that probability that at least one is green?   

Answer 1

$$\dbinom{3}{1}\dbinom{4}{4}=3(1)=3$$

$$\dbinom{3}{2}\dbinom{4}{3}=3(4)=12$$

$$\dbinom{3}{3}\dbinom{4}{2}=1(6)=6$$

$$3+4+3=10$$

$$\dbinom{10}{5}=252$$

$$P(at\ least\ 1 \ green)=1-\dfrac{3+12+6}{252}=\dfrac{11}{12}$$