Consider a state lottery where you get to choose 8 numbers from 1 to 80, no repetition allowed. The Lottery Commission chooses 11 from those 80 numbers, again no repetition. You win the lottery if at least 7 of your numbers are there in the 11 chosen by the Lottery Commission. What is the probability of winning the lottery?
I just wanted to check if what I am thinking is correct or not.
Sample size = $80 \choose 8$
Winning Events = $11 \choose 7$ * $73\choose 1$ $~$ $\bigg($i.e. $11\choose7$ if at least 7 number matches and $73\choose 1$ for $8^{th}$ number can be anything $\bigg)$
Therefore, the probability is given by:
$$ P = \frac{{11 \choose 7} {73 \choose 1} }{80 \choose 8}$$
Sample size is OK but Winning Events = $${11 \choose 7} * {69\choose 1} +{11 \choose 8} * {69\choose 0} $$