Peter has one of each of the following coins in his pocket: a penny, a nickel, a dime, a quarter, and a half-dollar. Four of these coins are taken out of the pocket and the sum of their values is calculated. How many different sums are possible?

The different sum of the 4 coins from the list of 5 coins is an illustration of combination or selection. There are 5 different possible sums.

Given

--- number of coins

--- coins to be selected to calculate sum

For the sum of the coin value to be calculated, the 4 coins must be selected. This means combination.

So, we make use of:

This gives

Expand

Hence, there are 5 different possible sums.

Read more about combinations at:

link

10

Step-by-step explanation:

This is a combinations problem, involving factorials.

5!/3!*2!=5*4/2=20/2=10