C(45,7)*7 = (45!)/(38!*6!) = 317,657,340

Chance to win = (No. of winning guesses) divided by (No. of possible guesses)

If you guess 6 numbers out of 45, there are C(45,6) possible guesses.

Since there are 7 winning guesses (because of the Nosaf), the chance is 1 to C(45,6)/7, or one to 1,163,580.

Another way:

Chance to win = (No. of outcomes where you win) divided by (No. of possible outcomes)

You have selected 6 numbers, and there are 39 more possibilities for the 7th number (45 minus the 6 already chosen). So there are 39 outcomes where you will win.

In the lottery, they draw 7 numbers out of 45.

So the chances are one to C(45,7)/39,

which is the same.

Where is my mistake?