In one of the Massachusetts state lotteries, the winning number is chosen by picking six ping-pong balls from a bin containing balls labeled "$1$" through "$36$" to arrive at a sequence of six numbers between $1$ and $36$. Ping-pong balls are not replaced after they're chosen; that is, no number can appear twice in the sequence. How many possible outcomes are there?
Note that in this last exercise, the order in which the ping-pong balls are chosen is relevant.