Probability of winning second prize and third prize in a lottery
Solution 1:
There are $49{48 \choose 6}$ different draws. You can win second prize in $6\cdot 42=252$ ways-choose one of the non-special numbers to miss and $42$ ways to pick the undrawn number. You can win third prize in ${6 \choose 2}{42 \choose 2}=12915$ ways. So the chances are second prize about $4.2\cdot 10^{-7},$ third prize about $2\cdot 10^{-5}$