Answer
The required solution is $\frac{1}{175711536}$
Work Step by Step
Assume the probability of a player winning the jackpot is $ P\left( E \right)$.
We know that is equal to, $ P\left( E \right)=\frac{\text{number of ways winning lottery}}{\text{total number of possible combinations}}$
Firstly, determine the number of ways of selecting white balls.
There are 56 white balls; selection of 5 white ball can be done as given below:
$\begin{align}
& {}^{56}{{C}_{5}}=\frac{56!}{\left( 56-5 \right)!5!} \\
& =\frac{56!}{51!5!} \\
& =\frac{56\cdot 55\cdot 54\cdot 53\cdot 52}{5\cdot 4\cdot 3\cdot 2\cdot 1} \\
& =3819816
\end{align}$
Then, determine the number of ways of selecting golden balls.
As there are 46 balls, selection of 1 golden ball can be done as:
$\begin{align}
& {}^{46}{{C}_{1}}=\frac{46!}{\left( 46-1 \right)!1!} \\
& =\frac{46!}{45!1!} \\
& =\frac{46\cdot 45!}{45!} \\
& =46
\end{align}$
Thus, the total number of possible combinations of balls is:
$^{46}{{C}_{1}}{{\cdot }^{56}}{{C}_{5}}=175711536$
Hence, $\frac{1}{175711536}$
