Question

A group of 10 students is used for an experimental study. The group comprises of 3 students with blood type O, 4 with blood type A, and 3 with blood type B. What is the probability that a random sample of 5 will contain 1 student with blood type O, 2 students with blood type A, and 2 students with blood type B?

Answer 1

P(one student with blood type 'O', 2 with type 'A' and 2 with blood type 'B') $= \frac{3C_1 \times 4C_2 \times 3C_2 }{ 10C_5 }$

$= \frac{3 \times 6 \times 3 }{ 252} \\ = \frac{3}{14}$