Question

a game has a deck of cards with 10 red cards, 4 blue cards, and 2 yellow cards. you randomly choose two cards(choose one and choose the second one without replacement) find the probability of choosing a blue card and a yellow card

Answer 1

$\displaystyle |\Omega|=\binom{16}{2}=\dfrac{16!}{2!14!}=\dfrac{15\cdot16}{2}=120\\ |A|=4\cdot2=8\\\\ P(A)=\dfrac{8}{120}=\dfrac{1}{15}\approx7\%$