There are 10·9/2 = 45 ways to choose 2 winners from 10 entrants.
There are 5·4/2 = 10 ways to choose 2 winners from Pike.
The probability that both winners are from Pike is 10/45 = 2/9.
_____
There are n ways to choose the first winner from a pool of n. There are n-1 ways to choose the second one, hence n(n-1) ways to choose two from n when order matters. Since this counts the choices (1)(2) and (2)(1) as two different possibilities, we need to divide by 2 when order doesn't matter.
