The American Mega Millions lottery, at the time of writing, involves the selection of five numbers out of 75 and one from 15. The jackpot is shared among the players who match all of their numbers in a corresponding random draw. What is the probability of winning the jackpot? Write a single line of Python code using NumPy to pick a set of random numbers for a player.
The probability of winning is one in \begin{align*} \left(\begin{array}{c}75 \\ 5\end{array}\right)\left(\begin{array}{c}15 \\ 1\end{array}\right) = \frac{75\cdot 74\cdot 73 \cdot 72\cdot 71}{1 \cdot 2\cdot 3 \cdot 4\cdot 5} \cdot 15 = 258890850 \end{align*} To pick five random numbers from 1-75 and one from 1-15:
In [x]: (sorted(np.random.choice(np.arange(1,76), 5, replace=False)),\
np.random.randint(15)+1)
([4, 21, 35, 36, 64], 14)