1. **Problem statement:** We have 7 shortlisted applicants and 3 different internship roles. We want to find how many different ways the roles can be assigned when the order of appointment matters. 2. **Formula used:** Since order matters and roles are distinct, this is a permutation problem. The number of ways to assign $k$ roles from $n$ applicants is given by the permutation formula: $$P(n,k) = \frac{n!}{(n-k)!}$$ 3. **Apply the formula:** Here, $n=7$ and $k=3$. $$P(7,3) = \frac{7!}{(7-3)!} = \frac{7!}{4!}$$ 4. **Calculate factorial values:** $$7! = 7 \times 6 \times 5 \times 4!$$ So, $$P(7,3) = \frac{7 \times 6 \times 5 \times 4!}{4!} = 7 \times 6 \times 5 = 210$$ 5. **Interpretation:** There are 210 different ways to assign the 3 roles to 7 applicants when order matters. **Final answer:** 210 (Option C)