When the roots of the polynomial

$$P(x)=(x-1)^{1}(x-2)^{2}(x-3)^{3} \cdots(x-10)^{10}$$

are removed from the real number line, what remains is the union of 11 disjoint open intervals. On how many of these intervals is P(x) positive?

**Answer Choices**

A. 3

B. 7

C. 6

D. 4

E. 5