You work as a health inspector and must visit each of the 15 restaurants in town once each week. In how many different orders can you make these inspections?

Answer: 15! or 1307674368000

Step-by-step explanation:

According to the permutations, if we arrange n things in order, then the total number of ways to arrange them = n!

Similarly, when health inspector inspects 15 restaurants in town once each week, the number of different orders can be made for these inspections = 15!

= 15 x 14 x 13 x 12 x 11 x 10 x 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1

=1307674368000

Hence, the number of different orders can be made for these inspections = 15! = 1307674368000