There are 10 bicyclists entered in a race. In how many different orders could these 10 bicyclist finish?
10! is the answer.
this is just like you are given 10 lines on a paper and you have to arrange 10 names on those 10 lines in all different ways .
so , starting with the lowermost line, you can put one of 10 names on that line and then on the line above that you can put 1 of 9 names and so on .
so the total ways to arrange all the names on those lines in all ways will be :