lotte odds calculation

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a lotto consists of 45 numbers. 8 numbers are randomly drawn and the first 6 number are winning numbers while the remaining 2 are supplementary numbers
a winning combination is 2 supp numbers plus 1 or 2 winning numbers.the question is the probability of this winning combination
solution manual says 144:1
my work is
(C(6,1)*C(39,5)/C(45,6)) * (C(2,2)/C(34,2)) + ( C(6,2)*C(39,4)/C(45,6)) *(C(2,2)/C(35,2))
and clearly wrong

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@Henryyyy,

How many numbers does the player pick?

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@markr,

Looks like 6. Here's the solution:

[C(2,2)*C(6,1)*C(37,3) + C(2,2)*C(6,2)*C(37,2)] / C(45,6)

C(2,2)*C(6,1)*C(37,3) is the number of ways to pick both supplementary numbers, 1 winning number, and 3 other numbers.

C(2,2)*C(6,2)*C(37,2) is the number of ways to pick both supplementary numbers, 2 winning numbers, and 2 other numbers.

C(45,6) is the number of ways to pick 6 numbers.

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@markr,

thanks markr, really appreciate it.
It is 6. I just assumed 8 cuz there is a misleading prize (5 winning numbers+1 or 2 supp numbers) in the winning combinations list. Bad worded question.

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lotte odds calculation

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