Picking 6 numbers out of 49, where you make exactly 6 picks to get those 6 winning numbers, where all 49 possible numbers are different, picked numbers can't be repeated, and the order in which the numbers are picked doesn't matter:
P(first picked number is a winner) = 6/49
P(2nd picked number is a winner) = 5/48
P(3rd picked number is a winner) = 4/47
P(4th picked number is a winner) = 3/46
P(5th picked number is a winner) = 2/45
P(6th picked number is a winner) = 1/44
P(all 6 of the above events happen) = 6/49 * 5/48 * 4/47 * 3/46 * 2/45 * 1/44
P(all 6 of the above events happen) = (6 * 5 * 4 * 3 * 2 * 1) / (49 * 48 * 47 * 46 * 45 * 44)
P(all 6 of the above events happen) = 43! * 6! / 49!
P(all 6 of the above events happen) = "49 choose 6"
P(all 6 of the above events happen) = 49 nCr 6 (on a calculator)
P(all 6 of the above events happen) = 0.0000000715112384 (about 1 in 13 million)