I was doing a factorial for the Euromillions:

It is effectively two 'draws'

In the first there are fifty numbers and the player must select the first five chosen.

50!÷((50-5)! x 5!)

I get 2,118,760

In order to win the main jackpot the player must now win a second draw

There are twelve numbers and the player must select the first two chosen.

12!÷((12-10)! x 2!)

66

2,118,760 x 66 = 139,838,160

And this is the value given on the wikipedia page.

But when I attempt to calculate the second prize probability I can't get it to come out.

The second prize is given to the players who select only one of the two numbers drawn from the second pool of twelve.

12!÷(((12-10)! x 2!) + (12-10)! x 2!))) =33

Because you get two goes with the second draw I sum the factorials on the right hand side and 33 has a nice connection to 66 and 'looks good' to me (though I have no intuitive sense for numbers).

2,118,760 x 33 =69,919,080

Similar to 1 in 6,991,908 on the wikipedia page for the Euromillions EXCEPT for the fact that I am out by a factor of 10!

SO where is my mistake?

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