How much cash is in the wallet In the wallet we have $26$ banknotes. If we take, arbitrarily, $20$ of them we are sure that we have at least one of $\$5$, at least two of $\$10$ and at least five of $\$20$. How much cash is in the wallet?
I have tried determining the number of compositions of $20$ in three parts with regard to the restrictions. Also tried using normal generating functions and obtaining coefficient next to $x^{20}$, but I don't see where does that get me. Any help or advice is appreciated.

The problem is much simpler. If we take 20 of the 26 notes, and we have at least five $\$20$ notes, then there must be at least eleven $ \$20$ notes (since otherwise the guarantee does not work). For similar reasons, there must be at least seven $ \$5$ notes, and at least eight $ \$10$ notes. Because $11+7+8 = 26$, this is all the notes in the wallet, and the total amount of cash is $\$(7\times 5 + 8 \times 10 + 11 \times 20)$.
