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In the lottery there are 5 numbers rolled from 35 numbers and for 3 right quessed numbers there is a third price. What's the propability that we will win the third price if we buy one ticket with 5 numbers.

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    Check the comment of Ross Millikan, he did the question assuming you need to get exactly $3$ right. Do similarily for exactly $4$ right and exactly $5$ right. Then you get total no of favourable outcomes. Alternatively, find the complementary probability, i.e getting less than $3$ as that would be easier..2012-11-11

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Hint: There are ${ 35 \choose 5}$ total draws. To get specifically third prize, you need to select $3$ of your $5$ and $2$ of the other $30$.

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    @user12392: for the ${30 \choose 2}$ see André Nicolas' comment to the other answer. He gives some good examples.2012-11-11
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Choose 5 from 35 in $\binom{35}{5}$ and from 5 numbers to get 3 exists $\binom{5}{3}=10$ possibilities and 2 other numbers you choose from 30 others thats not are in your ticket in $\binom{30}{2}=435 $ ways so total ways to win third place is $10\times435=4350$ ways.

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    There are many many tickets that will get you a third prize. If the numbers drawn are $1,2,3,4,5$, you will win third prize with $2,3,4, 7,11$ but also with $2,3,4, 12,20$ and with $2,3,4, 31,33$, and so on.2012-11-11