Question

in a competition 5 figure skaters will skate in a randomely assigned order. why can't you evaluate the product 5*5*5*5*5 to find the number of possible orders in which the skaters can skate

Answer 1

there are 5 skaters sitting in a penalty box.
A B C D E
You pull one out at random.
Say it is C and our chance is 1/5 for picking C
NOW WE HAVE 4
A B D E
Say it is A and our chance is 1/4 for picking A ( NOT 1/5 !!!!)
Next we pick B (1/3)
Next D (1/2)
Next E (1/1 or 1)
SO
our chances of picking that order are
(1/5)(1/4)(1/3)(1/2)(1/1)
or
1/5!
SO
and the number of possible orders is
5! = 120