answer all questions with explanation

(3 points) In a certain state-run lottery game, the purchaser of a ticket selects 4 numbers from 1 to 40, without any repeats, and then one number from 1 to 30 (that can be a repeat of the first four.) The first 4 numbers are selected randomly at a state drawing by selecting numbered balls from one bin, without replacement (the bin starts with 40 balls, numbered 1 to 40 of course) and then the 5th ball is called the "golden ball" and is randomly selected from another bin containing 30 balls, numbered 1 to 30. A winner of the prize can have the first 4 numbers in any order, and must also match the "golden ball" number. Calculate the probability of winning with just one ticket, leave it as a fraction of integers