Question

The probability of winning a 5/25 lottery game where 5 numbers are picked from a range of 25 is ________.

Answer 1

5 numbers chosen from 25 can be done in 25C5 = 25!/(5!*20!) = 53,130 ways. The probability of choosing the correct set of 5 numbers is
  1/53,130

Answer 2

$\displaystyle |\Omega|=\binom{25}{5}=\dfrac{25!}{5!20!}=\dfrac{21\cdot22\cdot23\cdot24\cdot25}{2\cdot3\cdot4\cdot5}=53130\\ |A|=1\\\\ P(A)=\dfrac{1}{53130}\approx0.002\%$