There are 9 possible choices for the first person in line. After that, there are 8 different choices for the second slot, so there are 9x8=72 ways just arranging people in the first two positions. Continuing, there are 7 choices for the third position, 6 left for the fourth, etc. Overall, it looks like 9*8*7*6*5*4*3*2*1, or 362,880 ways of arranging the people.
Hope that helps