(a) A company that makes crayons is trying to decide which 5 colors to include in a promotional mini-box of 5 crayons. The company can choose the 5 mini-box colors from its collection of 75 colors. How many mini-boxes are possible? (b) A certain committee consists of 18 people. From the committee, a president, a vice-president, and a treasurer are to be chosen. In how many ways can these 3 offices be filled? Assume that a committee member can hold at most one of these offices.

Step 1 ：Define the problem as a combination problem for part (a) and a permutation problem for part (b).

Step 2 ：For part (a), we are choosing 5 colors out of 75. Use the combination formula \(C(n, k) = \frac{n!}{k!(n-k)!}\), where n is the total number of items, k is the number of items to choose, and '!' denotes factorial.

Step 3 ：For part (b), we are choosing 3 people out of 18 to fill specific roles. Use the permutation formula \(P(n, k) = \frac{n!}{(n-k)!}\), where n is the total number of items, k is the number of items to choose, and '!' denotes factorial.

Step 4 ：Calculate the number of combinations for part (a) using the formula with n=75 and k=5. The result is 17259390.

Step 5 ：Calculate the number of permutations for part (b) using the formula with n=18 and k=3. The result is 4896.

Step 6 ：Final Answer: For part (a), the number of possible mini-boxes is \(\boxed{17259390}\). For part (b), the number of ways the offices can be filled is \(\boxed{4896}\).