A lottery game involves drawing 5 numbers from 1 to 30. Determine the probability of winning each of the the following prizes: First prize features 500,000 $ worth of cash, and all five numbers have to be matched. Second prize features 100,000 $ worth of cash, four numbers have to be matched. Third Prize features 100 $ worth of cash, three numbers have to be matched.

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In the lottery game described a prize of $500000 is won when all the five numbers match the numbers from 1 to 30.

The probability that a number matches the first number drawn is `1/30` . The probability that the second number matches is `1/29` . Similarly for the other three numbers the probability is `1/28` , `1/27` , `1/26` .

This gives the probability of winning the first prize as `1/(30*29*28*27*26) ~~ 5.84*10^-8 `

The probability of winning the second prize is `C(5,4)*(1/(30*29*28*27))*(25/26) ~~ 7.3*10^-6`

The probability of winning the third prize is : `C(5, 3)*1/(30*29*28)*(26/27)*(25/26) ~~ 3.8*10^-4`

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