How do I answer this probability question?

Question

Hot Lotto is played in District of Columbia, Iowa, Kansas, Minnesota, Montana, New Hampshire, New Mexico, North Dakota, South Dakota, or West Virginia. Players pick five numbered white balls from 1 to 39 and one numbered orange “hot ball” from 1 to 19. What is the probability of winning the jackpot? (Hint: Find the probability of picking the five numbered balls from 1 to 39 and multiply your answer by the probability of picking one from 1 to 19.)

Answer 1

Number of ways to pick 5 from 39 = 39!/(5!34!) = 575,757

Odds of picking 5 from 39 = 1/575757

Odds of picking 1 from 19 = 1/19

Odds of winning = 1/575757*1/19 = 1/10,939,383 = 0.0000091413%