Question

A bag contains 3 red marbles and 4 blue marbles. Two marbles are drawn at random without replacement. What is the probability they will both be blue?

Answer 1

$P(A)=\dfrac{C(4,2)}{C(7,2)}\\\\ P(A)=\dfrac{\dfrac{4!}{2!2!}}{\dfrac{7!}{2!5!}}\\\\ P(A)=\dfrac{4!}{2!2!}\cdot\dfrac{2!5!}{7!}\\ P(A)=3\cdot4\cdot\dfrac{1}{6\cdot7}\\ P(A)=\dfrac{2}{7}$