The number of sequences of ten terms, whose terms are either 0 or 1 or 2, that contain exactly five 1s and exactly three 2s, is equal to:

We need to find the number of sequences of ten terms, where each term is 0, 1, or 2, containing exactly five 1s and exactly three 2s.

Since the sequence has 10 terms with exactly five 1s and exactly three 2s, the remaining $$10 - 5 - 3 = 2$$ terms must be 0s.

We need to choose positions for the 1s, 2s, and 0s among the 10 positions. This is a multinomial coefficient:

$$\frac{10!}{5! \cdot 3! \cdot 2!}$$

Computing this: $$\frac{10!}{5! \cdot 3! \cdot 2!} = \frac{3628800}{120 \cdot 6 \cdot 2} = \frac{3628800}{1440} = 2520$$.

Hence, the correct answer is Option C.