1. ## Permutations

Determine how many different positive monetary amounts can be formed using any combination of two nickels and five dimes.

How do you found out all the amounts that can be formed by two different combinations?

2. This graphic answers the question.

3. I'm not sure I understand that. Could you elaborate?

4. Originally Posted by chengbin
I'm not sure I understand that. Could you elaborate?
The exponents are the amounts possible using two nickels and five dimes.
The coefficients tell you how many ways it is possible.
Look at $2x^{20}$. That tells us there are two ways to get the amount 20cents: two dimes or one dime and two nickels.
Whereas, $x^{25}$ tells us there is only one way to get the amount 25cents: two dimes and one nickel.

5. There isn't a simpler, faster way to do it other than expanding a summation?

6. Originally Posted by chengbin
There isn't a simpler, faster way to do it other than expanding a summation?
Look at the orginal question.
Originally Posted by chengbin
Determine how many different positive monetary amounts can be formed using any combination of two nickels and five dimes.
The answer is 12. There are 12 multiples of five from 5 to 60.
Usings nickels and dimes, all the amounts are multiples of five.