In Exercises 5–36, express all probabilities as fractions.

Change for a Quarter How many different ways can you make change for a quarter? (Different arrangements of the same coins are not counted separately.)

A quarter is to be formed using change.

The number of possibilities in which an event can occur happen are counted according as per the underlying conditions of the experiment.

The most convenient method is tocount the entire set of combinations once they are listed.

The value of a quarter is $0.25.

Only three coins that are less than a quarter are a nickel ($0.05), a penny ($0.01) and a dime ($0.10), combination of which can be used to provide the value equivalent to a quarter.

The number of ways in which a quarter can be made is listed below:

$2\left(0.10\right)+1\left(0.05\right)=0.25$

$2\left(0.10\right)+5\left(0.01\right)=0.25$

$1\left(0.10\right)+3\left(0.05\right)=0.25$

$1\left(0.10\right)+2\left(0.05\right)+5\left(0.01\right)=0.25$

$1\left(0.10\right)+1\left(0.05\right)+10\left(0.01\right)=0.25$

$1\left(0.10\right)+15\left(0.01\right)=0.25$

$5\left(0.05\right)=0.25$

$4\left(0.05\right)+5\left(0.01\right)=0.25$

$3\left(0.05\right)+10\left(0.01\right)=0.25$

$2\left(0.05\right)+15\left(0.01\right)=0.25$

$1\left(0.05\right)+20\left(0.01\right)=0.25$

$25\left(0.01\right)=0.25$

Therefore, there are 12 ways to make a quarter using nickels, dimes and pennies.