Answer
$P(winning~Mega~Millions)=\frac{1}{175,711,536}\approx0.000000005691$
Work Step by Step
First urn: the order in which the numbers are chosen does not matter. So, there are $_{56}C_5$ possibilities.
Second urn: there are 46 possibilities.
To find $N(S)$ use the Multiplication Rule:
$N(S)=_{56}C_5\times46=\frac{56!}{5!(56-5)!}\times46=\frac{56!}{5!\times51!}\times46$
But, $56!=56\times55\times54\times53\times52\times(51\times50\times49\times...\times3\times2\times1)=56\times55\times54\times53\times52\times51!$
$N(S)=_{56}C_5\times46=\frac{56\times55\times54\times53\times52\times51!}{5!\times51!}\times46=\frac{56\times55\times54\times53\times52}{5\times4\times3\times2\times1}\times46=175,711,536$
With a single ticket: $N(winning~Mega~Millions)=1$
Using the Classical Method (page 259):
$P(winning~Mega~Millions)=\frac{N(winning~Mega~Millions)}{N(S)}\frac{1}{175,711,536}\approx0.000000005691$
