Sorry Kaiser, but you have not addressed the challenge you originally set. You have not explained your answer, to say you looked it up in a table does not explain anything to someone who is not already familiar.
The first thing to consider is in how many ways can 6 numbers be chosen from 45. Those numbers are way to big to illustrate, so lets ask how many ways can we choose 2 letters from 4. For example a,b,c,d. Well the possibilities are ab,ac,ad,bc,bd,cd. That is 6 possibilities. You can try yourself to see if there are any others (I don't think you will find any).
This is calculated as 4 choices for the first letter, (a or b or c or d) then there are 3 choices for the second (you cannot choose the same one again). So that gives us 12 possibilities 4x3=12. However some of these are the same ab is the same choice as ba.
So we need to divide by the number of ways we have double counted the first choice 2 and the second choice 1.
The answer is 4x3 divided by 2x1 =6
Similarly the number of ways we could choose 3 out of 8 is 8x7x6 divided by 3x2x1 = 56
Or the number of ways to choose 6 from 2 million is
2,000,000 x 1,999,999 x 1,999,998 x 1,999,997 x 1,999,996 x 1,999,995 divided by 6 x 5 x 4 x 3 x 2 x 1 all of which is equal to 8.8888222e34 or approx 8 with 34 zeros after it.
That very large number is the number of ways the winning numbers could appear out of the drum.
The next issue is the chances of getting any one number correct. This is 1 divided by 45. Just like the probability of getting a coin toss correct is 1 divided by 2.
What are the chances of getting two coin tosses correct. Each one is a half, the probability if two in a row is a half multiplied by a half, thats a quarter. To illustrate, say you guessed two heads, well the possible results of tossing a coin twice are HH,HT,TH,TT. One out four of these results matches your guess.
So the probability of getting 6 correct out of 45, is 1 divided by 45 multiplied by itself 6 times. That is 1 in 8,145,060. The probability of 6 people getting this is this number multiplied by itself 6 times.
What about the probability of not getting 1 correct out of 45 that is 1-(1/8,145,060). In other words if there is 1 chance in 45 of a correct number then chances of an incorrect number is 1 minus 1 in 8,145,060. And this could happen not 6 ways but 2m minus 6 that is 1,999,994. So (1-(1/8,145,060)) multiplied by itself 1,999,994 times. That works out as 0.782276684
So the chance of there being exactly 6 winners is 8.88882222e34 x (1\8,145,060)^6 x 0.782276634 = 0.000000238 or 1 in 4,199,147
In summary
The number of possible results from 2,000,000 lines is 8.88882222 by 10 to the 34
The chances of getting any one number correct 1 in 45. Of getting each of the six correct is 1 in 45 multiplied by itself 6 times, or 1 in 8,145,060
The chances of 6 people getting each of the six correct is that multiplied by itself 6 times
We need to allow for the probability of not getting 1 correct from the 45 which is 0.782276634
So as above
8.88882222e34 x (1\8,145,060)^6 x 0.782276634 = 0.000000238 or 1 in 4,199,147
This is the probability of their being exactly 6 winners.