i have 5 coins,a penny,nickel,dime,quarter and loonie. how many different amounts of money can i pay using any combination of the coins?
I can use the penny in two ways, that is, either use it or not use it.
The same goes for the other 4 coins
So the number of ways is
2x2x2x2x2 = 32
but that includes not using any coins, which would not be an "amount of money"
so the number of ways is 31
To determine the number of different amounts of money you can pay using any combination of the five coins (penny, nickel, dime, quarter, and loonie), you can approach this problem systematically.
Step 1: Start with the smallest possible amount, which is zero. This means not using any coins.
Step 2: Consider using only one coin at a time. You have five choices: penny, nickel, dime, quarter, or loonie. Therefore, you can pay a total of five different amounts using just one coin (0.01, 0.05, 0.10, 0.25, or 1.00 in currency value).
Step 3: Continue by using two coins. You can pair up each coin with the remaining coins to create unique combinations. Here are the possibilities:
- Penny + Nickel = 0.06
- Penny + Dime = 0.11
- Penny + Quarter = 0.26
- Penny + Loonie = 1.01
- Nickel + Dime = 0.15
- Nickel + Quarter = 0.30
- Nickel + Loonie = 1.05
- Dime + Quarter = 0.35
- Dime + Loonie = 1.10
- Quarter + Loonie = 1.25
In total, there are 10 different amounts you can pay using two coins.
Step 4: For three coins, you can create combinations using the remaining three coins (excluding the first coin you have used). Here are the possibilities:
- Penny + Nickel + Dime = 0.16
- Penny + Nickel + Quarter = 0.31
- Penny + Nickel + Loonie = 1.06
- Penny + Dime + Quarter = 0.36
- Penny + Dime + Loonie = 1.11
- Penny + Quarter + Loonie = 1.26
- Nickel + Dime + Quarter = 0.40
- Nickel + Dime + Loonie = 1.15
- Nickel + Quarter + Loonie = 1.30
- Dime + Quarter + Loonie = 1.35
In total, there are 10 different amounts you can pay using three coins.
Step 5: For four coins, you can create combinations using the remaining two coins (excluding the two coins you have used). Here are the possibilities:
- Penny + Nickel + Dime + Quarter = 0.41
- Penny + Nickel + Dime + Loonie = 1.16
- Penny + Nickel + Quarter + Loonie = 1.31
- Penny + Dime + Quarter + Loonie = 1.36
- Nickel + Dime + Quarter + Loonie = 1.50
In total, there are 5 different amounts you can pay using four coins.
Step 6: For all five coins, you can create a single combination:
- Penny + Nickel + Dime + Quarter + Loonie = 1.51
In total, there is 1 different amount you can pay using all five coins.
By summing up these numbers, you have a total of 5 + 10 + 10 + 5 + 1 = 31 different amounts of money that can be paid using any combination of the given five coins.