Answer to Question #200290 in Statistics and Probability for Ja'khi

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

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

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

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

$3+4+3=10$

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

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