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?
"P={4\\above{1pt}11}\u00d7{5\\above{1pt}10}+{5\\above{1pt}11}\u00d7{2\\above{1pt}10}+{4\\above{1pt}11}\u00d7{2\\above{1pt}10}+{2\\above{1pt}11}\u00d7{4\\above{1pt}10}+{2\\above{1pt}11}\u00d7{5\\above{1pt}10}+{5\\above{1pt}11}\u00d7{4\\above{1pt}10}=2\u00d7\\lparen{20\\above{1pt}110}+{10\\above{1pt}110}+{8\\above{1pt}110}\\rparen={76\\above{1pt}110}=0.69"
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