How many different ways can a building inspector visit 7 new construction sites in an area where there are 10 new construction

To solve this problem, we can use the concept of permutations. Since the order in which the building inspector visits the construction sites matters, we can use the formula for permutations:

nPr = \frac{n!}{(n-r)!}

where n is the total number of new construction sites (10 in this case) and r is the number of construction sites the building inspector visits (7 in this case).

Plugging in the values:

10P7 = \frac{10!}{(10-7)!} = \frac{10!}{3!} = \frac{10*9*8*7*6*5*4*3*2*1}{3*2*1} = 604800

So, there are \boxed{604800} different ways the building inspector can visit 7 new construction sites out of a total of 10 construction sites.

\boxed{Answer: 604800}