I went and re-read that wizard of odds page that you linked to john and i found this

"The overall general formula for the probability of x matches and y marks is combin(y,x)*combin(80-y,20-x)/combin(80,20).

As an example let's find the probability of getting 4 matches given that 7 were chosen. This would be the product of combin(7,4) and combin(73,16) divided by combin(80,20). combin(7,4) = 7!/(4!*3!)= 35. combin(73,16) = 73!/(16!*57!)=5271759063474610. combin(80,20) = 3535316142212170000. The probability is thus (35*5271759063474610)/3535316142212170000 =~ 0.052190967 ."

in the game of his example there are a total of 80 numbers and the operator chooses 20, thus the denominator of 80C20. but note that the numerator is built upon the number of "marks" made by the bettor and the number of matches out of the 20. the marks are the numbers selected by the player. so for his example:

total numbers 80

operator selects 20

player selects 7 = y

player matches 4 = x

so for the situation of this problem 80 becomes 50, 20 becomes 8, the 7 numbers selected becomes 5 and the 4 matches becomes 5.

thus his formula is

combin(5,5)*combin(45,3)/combin(50,8)

which my calculator show to be .0000264, the original poster's value.

in your original response you wrote

"y = number chosen = 8"

y in that formula should be the number chosen by the player. you let that be the number chosen by the operator, and so did i on my previous post. in this porblem the number chosen by the player is 5 and the number chosen by the house is 8. i still think something is not right here, i'll remain unconvinced for now that any of these potential answers is correct.

how did you set up your simulation? it does seemto matchup with your calculation.

cheers

jerry