Let S = {c,i,p, h, e,r, s}. Let A be the set of permutations of S in which i and e appear consecutively (in the order ie). Let B be the set of permutations of S in which h and i appear consecutively. Let C be the set of permutations of Sin which p and h appear consecutively. • In order to find [A], how many permutations of S are there in which i and e appear consecutively, we define a new set P and find the permutations of it. What is P and what is [P? What is |A|? • In order to find |An B, permutations of S in which i and e and h and i appear consecutively, we define a new set Q and find the permutations of Q. What is Q and Q? What is An B? • What is AU B|?

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A: See the handwritten solution

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