permutations and combinations (forming a committee)

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If 3 students are randomly chosen from a class of 30 to form a committee

(a) what is the total number of different committees that can be created?

Ans: Since order doesn't matter, use combination

$$C(30,3) = \frac{30!}{3!27!}$$

(b) If the first student chosen would be president, the second vice president, and the third be secretary, how many different ways can the committee be created?

Ans: Since order matter, use permutation

$$P(30,3) = C(30,3)\cdot 3!$$

Is the way I solved part (b) correct?