Question

seven runners are competing in a 100-meter race. in how many different ways can runners finish in first, second, and third place?

Answer 1

We use permutation as order is concerned.
n = 7, r = 3
nPr(7,3) = (n!)/(n - r)!
(7!)/(7-3)!
7*6*5*4*3*2*1 / 4*3*2*1 = 7*6*5 = 210.
So, in 210 different ways can runners finish in first, second and third place.