#### Answer

a) $\frac{1}{749398}$
b)$\frac{1}{10000}$
c) 10000

#### Work Step by Step

a) Because the order is not important, we can use the combination rule to determine the number of possibilities: $\frac{41!}{(41-5)!5!}=749398.$
We also know that $probability=\frac{number \ of \ good \ outcomes}{number\ of\ all\ outcomes}$, therefore $P=\frac{1}{749398}$.
b)By using the fundamental counting rule(knowing that there are 10 digits) we can get the number of possibilities: $10\cdot 10\cdot 10\cdot10=10000$. We also know that $probability=\frac{number \ of \ good \ outcomes}{number\ of\ all\ outcomes}$, therefore $P=\frac{1}{10000}$.
c) By using the properties of b), then 1 out of 10000 tickets is a winner, hence if there is no profit the return should be equal to the price of 10000 tickets which is 10000.