Five athletes are in a 100k race. How many different ways can they finish based on their order?

Answer 1

5! = 120 ways to finish

IF you don't count ties, which don't happen that much if you have photo finishes, seeing whose nose crossed the line first, by a hair. With 100K, they'll be so spread out, chances of a tie approach zero. And ignore one or more not finishing, dropping out before a full 100K. that' a real possibility though. A tornado comes out of nowhere and they're all toast. But still they drop out at different distances, so

then ignoring tragedies, tornadoes and ties

and cheaters getting disqualified, for taking short cuts or using drugs, lying about their age to get in a different age category, if they're not out of breath after 100K, they took a major short cut somewhere.

ABCDE, ABCED, ABDCE, ABDEC, ABECD, ABEDC 6 ways with A first, B second 3! = 6

ACBDE ...another 6 with A 1st C 2nd

ADBCE.... another 6

AEBCD.... another 6

24 with A 1st

24 with B 1st

24 with C 1st

24 with D 1st

24 with E 1st

that's 5 x 24 = 120 ways they could finish

5! of 120

5! = 5x4x3x2x1 = 120 for 5 runners

if there were 4 runners then 4! = 24 ways

3 runners 3! = 6 ways

2 runners 2! = 2 ways to finish

1 runner 1! way

6 runners, 6! = 720 ways