Picking 3 numbers out of 30, where you make exactly 3 picks to get those 3 winning numbers, where all 30 possible numbers are different, picked numbers can't be repeated, and the order in which the numbers are picked doesn't matter:
Buying 1 ticket:
P(first picked number is a winner) = 3/30
P(2nd picked number is a winner) = 2/29
P(3rd picked number is a winner) = 1/28
P(all 6 of the above events happen) = 3/30 * 2/29 * 1/28
P(all 6 of the above events happen) = (3 * 2 * 1) / (30 * 29 * 28)
P(all 6 of the above events happen) = 27! * 3! / 30!
P(all 6 of the above events happen) = "30 choose 3"
P(all 6 of the above events happen) = 30 nCr 3 (on a calculator)
P(all 6 of the above events happen) = 0.00024630541 (1 in 4060)