Question

Suppose there are three different types of cakes that are sold at Lina’s Bakery. There are 4 cheesecakes, 5 vanilla sponge cakes and 2 black forest cakes. Tom takes at random 2 of these cakes without replacement. What is the probability that he takes 2 different types of cakes upon his selection?

Answer 1

$P={4\above{1pt}11}×{5\above{1pt}10}+{5\above{1pt}11}×{2\above{1pt}10}+{4\above{1pt}11}×{2\above{1pt}10}+{2\above{1pt}11}×{4\above{1pt}10}+{2\above{1pt}11}×{5\above{1pt}10}+{5\above{1pt}11}×{4\above{1pt}10}=2×\lparen{20\above{1pt}110}+{10\above{1pt}110}+{8\above{1pt}110}\rparen={76\above{1pt}110}=0.69$