A purse contains 4 pennies, 2 nickels, I dime, and I quarter. Different values can be obtained by using one or more coins in the purse. How many different values can be obtained?
The answer is 49, this is a simple combinations problem.
Thank you. I just wanted to know if there was a faster way to do it.
Start listing them. Using the quarter, there are
q
qd, qnn
qdnn
qdp, qnnp
qdpp, qnnpp
and so on.
Now eliminate the quarter, and you get another list using the dime...
Lots more than 16 values.
how did you get that
To find out how many different values can be obtained from the coins in the purse, we need to consider all possible combinations of coins.
Let's break it down:
- We have 4 pennies. This means we can have 4 different values: 1 cent, 2 cents, 3 cents, and 4 cents.
- We have 2 nickels. A nickel is worth 5 cents. Using one or both nickels, we can have 3 additional values: 5 cents, 10 cents, and 15 cents.
- We have 1 dime, which is worth 10 cents. Adding this to the previous values we calculated, we can have 4 more values: 10 cents, 11 cents, 12 cents, and 14 cents.
- Finally, we have 1 quarter, which is worth 25 cents. Adding this to the previous values, we can have 4 more values: 25 cents, 26 cents, 28 cents, and 35 cents.
In total, we can obtain 4 + 3 + 4 = 11 different values by combining the coins in the purse.