Thad: I think the relevant quantities in context would be ten or more doubles and five or more boxcars. As far as your calcs go, I think the 10 doubles figure has to be multiplied by the combinations of 10 items chosen from 45, which I think is 45!/(10!*35!). A comparable adjustment needs to be made to the second calc, but I don't have time to work it out :-)
The chance of rolling exactly 10 doubles in 45 rolls is (1/6)^10 * (5/6)^35 * C (10, 45), where C (x, y) gives you the number of ways to pick x elements from a set of y elements. Rolling exactly 5 double sixes, and exactly 5 other doubles out of 45 rolls happens with chance (1/36)^5 * (5/36)^5 * C (5, 45) * C (5, 40).
The former is slightly less than 9%, the latter is slightly more than 0.1%.
(sakla) If you are waiting for your turn, click on "change" next to the "refresh" on the main page, then set refresh the page to 30 seconds to get your turn to move displayed faster. (Servant) (Bütün ipuçlarını göster)