you have 2 pennies, 3 nickels, 1 dime and 2 quarters. how many different sums of money can you make using one or more of these 8 coins
well, start listing them:
p = 1
n = 5
d = 10
q = 25
pp = 2
pn = 6
...
ppnnndqq = 77
Now count them up, after eliminating duplicate amounts
To find the number of different sums of money you can make using one or more of these 8 coins, we can use a combination of basic counting principles and mathematical calculations.
First, let's consider the possibilities individually for each type of coin.
1. Pennies: Since you have 2 pennies, you can have either 0, 1, or 2 pennies in a sum. So, there are 3 possibilities for pennies.
2. Nickels: Similarly, for the 3 nickels you have, you can have 0, 1, 2, or 3 nickels in a sum. This gives us 4 possibilities for nickels.
3. Dimes: With 1 dime, you can choose to have 0, 1, or 2 dimes in a sum, resulting in a total of 3 possibilities for dimes.
4. Quarters: Finally, you have 2 quarters, which means you can have 0, 1, or 2 quarters in a sum. This gives us 3 possibilities for quarters.
To find the total number of different sums, we need to calculate all the possible combinations of these individual possibilities. We multiply the number of possibilities for each type of coin because each coin is chosen independently.
Total number of possibilities = possibilities for pennies * possibilities for nickels * possibilities for dimes * possibilities for quarters
= 3 * 4 * 3 * 3
= 108
Therefore, you can make 108 different sums of money using one or more of these 8 coins.