Lara, Sara and Cara are good friends. They have a set of 12 cards each with one of the letters S, U, X, Y, E, O, T, I, H, A, V, B on them. For the purpose of this question, a word is any sequence of letters, regardless as to whether it makes any sense as a word in the English language and a sentence is any combination of words, regardless of whether it is meaningful. (a) First Lara randomly chooses one card. Then Sara randomly chooses 4 cards from the re- maining cards. Then Cara randomly chooses 3 cards from the remaining cards. Each girl puts their letters together in random order to form a word. Then they put their words to- gether to form a sentence, with Lara's word first, Sara's word second and Cara's word last. How many different outcomes of the sentence are possible? (b) Compare the result obtained in (a) to P(12, 8) and argue if you expect the two to be the same or why you expect them to differ? (short answer suffices) (c) What is the probability that the sentence resulting in (a) reads "I love you'? What is the probability that the sentence resulting in (a) reads 'T hate you"? (d) Instead of putting all three words together to form a sentence, the girls now randomly choose (for example by drawing sticks) one of their words and put that word on the table. How many different outcomes are possible