Question

There are 40 pieces of building blocks in a bag: 10 each of blue, green, red, and yellow. Two pieces are chosen at random. Identify the probability that both of the pieces chosen are green.

Answer 1

$\displaystyle |\Omega|=\binom{40}{2}=\dfrac{40!}{2!38!}=\dfrac{39\cdot40}{2}=780\\|A|=\binom{10}{2}=\dfrac{10!}{2!8!}=\dfrac{9\cdot10}{2}=45\\\\P(A)=\dfrac{45}{780}=\dfrac{3}{52}\approx5,8\%$