In a lottery, you must match all 6 numbers drawn at random from 1 to 40 without replacement to win the grand prize, 5 out of 6 numbers to win second prize, and 4 out of 6 numbers to win third. The ordering of the drawn numbers is irrelevant. Find the probability of winning each prize.
To win the grand prize, I think the probability is just 1/(40 Combination 6). How do you account for the fewer numbers drawn in the other two parts of the question though?