Answer to Question #235758 in Statistics and Probability for gajen

Question

There are 30 students in the group. The marks for the control test were the following: 8 students received “excellent” marks, 12 students - “good” marks, 8 students – “satisfactory”. What is the probability that 3 students invited for answer have “good” marks

Answer 1

$$P(3\ ''good'')=\dfrac{\dbinom{12}{3}\dbinom{30-12}{0}}{\dbinom{30}{3}}$$

$$=\dfrac{\dfrac{12!}{3!(12-3)!}(1)}{\dfrac{30!}{3!(30-27)!}}=\dfrac{220}{4060}=\dfrac{11}{203}$$