Florida lottery selection Florida lottery consists of 6 numbered balls from a bin containing 53 numbered balls. If you buy one ticket, you win a share of the grand prize if the 6 numbers you picked, in any order, matches the 6 chosen by the lottery official. What is the probability of winning a share of the grand prize with the purchase of a ticket?

There are $\dbinom{53}{6}$ ways for the Lottery Corporation to pick $6$ numbrs from the $53$. If the randomizing procedure is good, all these ways are equally likely.
Thus if you hold $1$ ticket, the probability your numbers match the Corporation's numbers is $\dfrac{1}{\binom{53}{6}}$. 
This is $\dfrac{(6)(5)(4)(3)(2)(1)}{(53)(52)(51)(50)(49)(48)}$. 
