Step 1: Count the total number of letters in the word "MARKETING". The word "MARKETING" has 9 letters: M, A, R, K, E, T, I, N, G. All the letters are distinct. Step 2: Calculate the number of permutations. Since all 9 letters are distinct, the number of possible permutations of these letters is $9!$. $$9! = 9 \times 8 \times 7 \times 6 \times 5 \times 4 \times 3 \times 2 \times 1$$ $$9! = 362,880$$ The final answer is $\boxed{362,880}$. --- Step 1: Identify the total number of distinct letters. The word "MARKETING" has 9 distinct letters. So, $n=9$. Step 2: Identify the number of letters to be arranged. We need to arrange any three letters, so $r=3$. Step 3: Calculate the number of arrangements using the permutation formula. The number of permutations of $n$ distinct items taken $r$ at a time is given by $P(n, r) = \frac{n!}{(n-r)!}$. $$P(9, 3) = \frac{9!}{(9-3)!} = \frac{9!}{6!}$$ $$P(9, 3) = \frac{9 \times 8 \times 7 \times 6!}{6!}$$ $$P(9, 3) = 9 \times 8 \times 7$$ $$P(9, 3) = 72 \times 7$$ $$P(9, 3) = 504$$ The final answer is $\boxed{504}$. --- Step 1: Identify the number of working days. The man works a five-day week, so there are 5 days. Step 2: Identify the number of travel options for each day. For each day, he can travel by foot, by cycle, or by bus. This gives 3 options. Step 3: Calculate the total number of ways to arrange a week of travel. Since the choice of travel for each day is independent, we multiply the number of options for each of the 5 days. Number of ways = (Options for Day 1) $\times$ (Options for Day 2) $\times$ (Options for Day 3) $\times$ (Options for Day 4) $\times$ (Options for Day 5) Number of ways = $3 \times 3 \times 3 \times 3 \times 3 = 3^5$ $$3^5 = 3 \times 3 \times 3 \times 3 \times 3 = 9 \times 9 \times 3 = 81 \times 3 = 243$$ The final answer is $\boxed{243}$.